How do you create a rotation matrix that will represent a rotation of angle theta about a vector (x,y,z)? This is instead of rotating about an axis.

33,940 results
  1. trig

    If sin theta is equal to 5/13 and theta is an angle in quadrant II find the value of cos theta, sec theta, tan theta, csc theta, cot theta.

  2. math

    1.A wind turbine has blades 50m in diameter and an overall height of 125m. If it has four blades instead of three, create four equations modelling the height of a point on the tip for each of the four blades. 2.Create a sine equation for the height of a

  3. Linear algebra

    please help me with this question I have no idea how to solve it, thanks Suppose T is a transformation from ℝ2 to ℝ2. Find the matrix A that induces T if T is rotation by 1/6π.

  4. Math

    Which of the following are necessary to describe a rotation of a figure on a coordinate plane ? A.the center of rotation B.the shape of the figure C.the number on of degrees of the rotation D.the direction of the rotation Is the answers A and C? thank you

  5. Maths - Polar coordinates

    The point (3, 2) is rotated 30 degrees about the origin. What are the polar coordinates of this after rotation? Am I right in saying it's (root13, 30)? The angle rotated and the radius calculated as root(3^2 + 2^2)? I can convert between polar and

  6. Math 10

    A trundle wheel can be used to measure the walking distance between two locations. a) If the diameter of a trundle wheel is 45 cm, how far will a person have walked when the wheel makes one full rotation? b) If a person walks for 0.7 km, how many times has

  7. trig

    Find csc(theta), tan (theta), and cos (theta), where theta is the angle shown in the figure. Give exact values, not decimal approximations c=10 b=7 a=7.14 the right angle is locate between sides a and b and the theta angle is an acutle angle sides b and c.

  8. Math

    18. Identify a sequence of transformations that maps triangle ABC onto triangle A′′B′′C′′ in the image below. (1 point) clockwise 90° rotation; enlargement counterclockwise 90° rotation; reduction counterclockwise 90° rotation; enlargement

  9. physics question

    As denizens of the surface of a spinning planet, we are always in uniform circular motion. Imagine you are in Nairobi (on the Earth's equator) at noon on a Monday. Answer the following questions only considering the rotation of the earth and NOT the

  10. math, PLEASE HELP!

    Point E(0, -2) is a vertex of square DEFG. After a 90* clockwise rotation of the square about the origin, which of the following is the location of E? A. (-2,0) B. (2,0) C. (2,2) D. (0,2) Point D(-3,5) is a vertex of triangle DEF. After rotation of the

  11. Diagonalize

    construct a nondiagonal 2 x 2 matrix that is diagonalizable but not invertible. Just write down a diagonal matrix with one zero on the diagonal and then apply an orthogonal transformation. E.g. if you start with the matrix: A = [1 ,0 0,1] And take the

  12. Physics- Someone Please Help!!!

    A luggage carousel at an airport has the form of a section of a large cone, steadily rotating about its vertical axis. Its metallic surface slopes downward toward the outside, making an angle of 21.0° with the horizontal. A 37.0 kg piece of luggage is

  13. Precalc

    Identify the graph of the equation. What is the angle of rotation for the equation? y^2+8x=0 is parabola 90 degrees correct? also Identify the graph of the equation. What is the angle of rotation for the equation? xy = -5 =hyperbola 45 degrees

  14. Physics

    A rotating space station has radius 1310 m, measured from the center of rotation to the outer deck where the crew lives. What should the period of rotation be if the crew is to feel that they weigh one-half their Earth weight?

  15. Chemistry

    The structure of Crestor (rosuvastatin), a medication used to reduce cholesterol, is shown below. If the specific rotation for this compound is known to be +100, what would be the specific rotation for the stereoisomer shown at the right?

  16. Physics

    Which of the following is the correct equation for Στ for the given rotation axis? All rotation axes lie on the x axis and torques that would cause a counterclockwise rotation are positive.

  17. Geometry

    Use the graph to answer the question. Parallelogram ABCD and its image. The coordinates of the vertices are listed in the long description. © 2016 FlipSwitch. Created using GeoGebra. Which series of transformations correctly maps parallelogram ABCD to

  18. differential calculus

    a SECURITY CAMERA is centered 50 feet above a 100-foot hallway. it is easiest to design the camera with a constant angular rate of rotation, but this results in a variable rate at which the images of the surveillance area are recorded. so, it is desirable

  19. Computer Science

    How do you create a rotation matrix that will represent a rotation of angle theta about a vector (x,y,z)? This is instead of rotating about an axis.

  20. math

    Find the entries of the following matrices: (a) the 2 ×2 matrix M for the reflection across the line y = x. (b) the 2 ×2 matrix N for the 90 degree counterclockwise rotation about the origin. (c) the product MN;what transformation does this represent?

  21. precalc pre ap

    If theta is a rotation angle that terminates in quadrant ll and sin of theta is 5/13, find cos of theta and tan of theta. Use the first Pythagorean identity to solve for cos of theta and use quotient identity to solve for tan of theta.

  22. Physics

    In an amusement park rocket ride, cars are suspended from L = 4.28-m cables attached to rotating arms at a distance of d = 6.10 m from the axis of rotation. The cables swing out at an angle of θ = 52.0° when the ride is operating. What is the angular

  23. Geometry

    1.1.Determine whether the regular pentagon has reflection symmetry, rotation symmetry, both, or neither. If it has reflection symmetry, state the number of axes of symmetry. If it has rotation symmetry, state the angle of rotation. For each type of

  24. Physics

    A rotating space station has radius 1270 m, measured from the center of rotation to the outer deck where the crew lives. What should the period of rotation be if the crew is to feel that they weigh one-half their Earth weight? I got 101.1 seconds... is

  25. physics

    The drawing shows two blocks that are placed at the ends of a massless board. The board is balanced on a support that serves as an axis of rotation. The block on the left has a mass of 5.8 kg. What is the moment of inertia of this system about the axis of

  26. Math30

    An angle with a negative rotation passes through the point(-5,-8). To, the nearest degree what is the measure of the angle?

  27. PreCalculus

    Problem: Identify the conic from the equation 13x^2-6(sq.rt.6)xy+7y^2-16=0 I have to choose from the following four answers: hyperbola (angle of rotation 45) hyperbla (angle of rotation 60) ellipse (angle of rotation 90) ellipse (angle of rotation 30) I

  28. math

    Describe the distance of point P from the far left or right of the center of the wheel as a function of the angle of the rotation. Assume that the wheel is rotating counterclockwise and the angle of rotation,theta, is the angle between the horizontal ray

  29. Pre-cal

    Describe the distance of point P from the far left or right of the center of the wheel as a function of the angle of the rotation. Assume that the wheel is rotating counterclockwise and the angle of rotation,theta, is the angle between the horizontal ray

  30. Orbital Mechanics

    Some help with this exercise please. If you could give an explanation and not only the answers it would be great!!! Besides the 3-2-1 rotation sequence, another very common sequence in spacecraft applications is the 3-1-3 rotation sequence in which the z

  31. algebra

    which of the following are necessary to describe a rotation of a figure on a coordinate plane? choose all that apply the center of rotation the shape of the figure the number of degrees of the rotation the direction of the rotation

  32. math

    1.A milling machine has a gear that spins, making one complete rotation counter clockwise every 360 milliseconds. The gear has a tooth with a marker in it as shown in the diagram below. There is a sensor 30mm below the center of the gear as viewed from the

  33. Linear Algebra

    Consider the linear transformation T: R^3->R^3 which acts by rotation around the y-axis by an angle of pi, followed by a shear in the x-direction by a factor of 2. a) Find the matrix for T. Explain your method. b) What is T(1,2,3) c) Without calculation,

  34. Chemistry

    If the specific rotation of Compound X is (-) 123.8º, what would be the observed rotation of its enantiomer, Compound Y, assuming the concentration and cell path length is the same? b. If a racemic mixture of Compound X and Compound Y were analyzed, what

  35. Organic Chemistry

    A 0.160 M solution of an enantiomerically pure chiral compound D has an observed rotation of 0.20° in a 1-dm sample container. The molar mass of the compound is 128.0 g/mol. (a) What is the specific rotation of D? (b) What is the observed rotation if this

  36. math

    A stirring blade is attached at the level of the center of the wheel. Find the distance from the center of the wheel to the stirrer blade for 30° and 225° angles of rotation. The radius is 2ft and the rod of the blade attached to the blade is 5ft long.

  37. math

    18. Identify a sequence of transformations that maps triangle ABC onto triangle A′′B′′C′′ in the image below. (1 point) clockwise 90° rotation; enlargement counterclockwise 90° rotation; reduction counterclockwise 90° rotation; enlargement

  38. Math--Fast Pleasee!

    Find the coordinate of the image of the point (3,6) rotated with respect to the x-axis and the y-axis. I plotted the points and came up with (3,-6) and (-3,6) The choices for the answer is a)(6,-3) b) (-6,3) c) (-3,-6) d) (0,-6) Was I wrong or what did i

  39. math

    What is the rule for finding coordinates after a 90 degree rotation? after a 180 degree rotation? after a 270 degree rotation?

  40. physics

    In an amusement park ride, cars are suspended from L = 4.22 m cables attached to rotating arms at a distance of D = 6.25 m from the axis of rotation. The cables swing out at an angle of θ = 49° when the ride is operating. What is the angular speed of

  41. Physics - angular acceleration

    An object rotates about a fixed axis, and th angular position of a reference line on the object is given by THETA(t)=0.4e^2t, where THETA is in radians, and t is in seconds. [a.] what is the object's angular acceleration at t = 2 s? ..this is my work so

  42. Linear Momentum in Rotational motion

    It is known that for a mass (m) that moves with velocity (v) the linear momentum is (m)x(v). Now, assume we have a rod of mass (m) and radius (R) that rotates with constant angular velocity (w). Also, isolate only half of the cycle (rotation for 180

  43. math

    Which sequence of transformations would yield a triangle similar to the original triangle but not congruent? A) rotation and dilation B) reflection and rotation C ) translation and rotation D) reflection and translation

  44. physics

    Determine the torques about the axis of rotation P produced by each of the four forces shown in the figure (Figure 1). All forces have magnitudes of 120 N and are exerted a distance of 2.0 m from P on some unshown object O. Determine the torque about the

  45. Trigonometry

    A variant on the carousel at a theme park is the swing ride. Swings are suspeneded from a rotating platform and move outward to form an angle x with the vertical as the ride rotates. The angle is related to the radial distance,r, in metres, from the centre

  46. Chemistry(Please help)

    I know that to calculate the specific rotation for a compound you do observed rotation / path length(dm) * conc. (g/ml). I am confused about how to calculate the specific optical rotation for a compound. Thank you for your help!

  47. Physics

    Here's the question again that I am trying to get help with because I can't figure it out and I got one answer, but I really couldn't understand it. Help please! A ferris wheel makes one rotation in 15 minutes. Find your car's location and the angle of

  48. mastering quantum mechanics

    Problem 3: Rotating a spin state (3 parts , 15 point) PART A (6 points possible) Consider the |+⟩ state of a spin one-half particle (as usual |±⟩=|z;±⟩) and apply to it the rotation operator R that rotates states by an angle θ around the y axis.

  49. physics

    the rotation of earth is a period of 86164 seconds. the earth has a radius of 6380 km. how fast would you be moving due to earths rotation at the equator? also how fast would you be moving at a latitude of 27 degrees north of the equator? also calculate

  50. MATH

    Figures that correspond under a translation, rotation, or reflection are said to be translation congruent, rotation congruent, or reflection congruent. Position two congruent figures on a piece of paper to satisfy each combination of congruences listed.

  51. Another astronomy (algebra-based physics) question

    I’d prefer thorough solutions, but if you can only provide formulas that would solve each part of the problem, that’d be helpful too :-) Thanks! Spinning too fast The rate of rotation of astrophysical objects that are held together by gravity (e.g.,

  52. geometry

    Figures that correspond under a translation, rotation, or reflection are said to be translation congruent, rotation congruent, or reflection congruent. Position two congruent figures on a piece of paper to satisfy each combination of congruences listed.

  53. Chemistry

    Organic chemistry: an attempt at synthesizing a certain optically active compound resulted in a mixture of its enantiomers. The mixture had an observed specific rotation of 11.0 degrees. If it is known that the specific rotation of the R enantiomer is

  54. trigonometry

    what direction of rotation generates and angle with a measure of -90 degrees? of 120 degrees? what portion of a complete rotation is -90 degrees? 120 degrees?

  55. Algebra(2 of 3)

    The vertices of ABC are A(-3,-4),B(-1,3),C(3,-2). The triangle is rotated 90 degrees counterclockwise. Use the rotation matrix [0 -1][1 0] to find the coordinates of C' A)(-3,2) B)(4,-3) C)(-3,-1) D)(2,3) I chose A [0 -1] x [-3 -1 3][-4 3 -2] =

  56. physics

    A limb, which is 1m long, moves through an angle of 30 degrees in 0.5 seconds. a) What is the average angular velocity of: i) Its end? ii) A point 30 cm from the axis of rotation? b) What is the linear velocity of: i) Its end? ii) A point 30 cm from the

  57. physics

    A limb, which is 1m long, moves through an angle of 30 degrees in 0.5 seconds. a) What is the average angular velocity of: i) Its end? ii) A point 30 cm from the axis of rotation? b) What is the linear velocity of: i) Its end? ii) A point 30 cm from the

  58. science

    how the earth rotates by itself? Momentum imparted to it million of years ago when the solar system formed. One theory involves glancing collision with a large asteroid millions of years ago that also broke off material that eventually developed into the

  59. physics

    pulsar is a rapidly rotating neutron star that emits radio pulses with precise synchronization, there being one such pulse for each rotation of the star. The period of rotation is found by measuring the time between pulses. At present, the pulsar in the

  60. Trigonometric Functions of Angles in Standard posi

    please help mee :( I want to pass my assignment but I dont get the lesson . 1. Create the following in a long sized paper with standard 1-inch margin. 2. Make an illustration of your hobby/ies that you love to do and identify the number of time you repeat

  61. Physics- Can someone please help me!!!

    A luggage carousel at an airport has the form of a section of a large cone, steadily rotating about its vertical axis. Its metallic surface slopes downward toward the outside, making an angle of 21.0° with the horizontal. A 37.0 kg piece of luggage is

  62. Physics- Elena please help! I'm so confused!!

    A luggage carousel at an airport has the form of a section of a large cone, steadily rotating about its vertical axis. Its metallic surface slopes downward toward the outside, making an angle of 21.0° with the horizontal. A 37.0 kg piece of luggage is

  63. Physics- Elena please help!

    A luggage carousel at an airport has the form of a section of a large cone, steadily rotating about its vertical axis. Its metallic surface slopes downward toward the outside, making an angle of 21.0° with the horizontal. A 37.0 kg piece of luggage is

  64. Physics- PLEASE HELP

    A luggage carousel at an airport has the form of a section of a large cone, steadily rotating about its vertical axis. Its metallic surface slopes downward toward the outside, making an angle of 21.0° with the horizontal. A 37.0 kg piece of luggage is

  65. math

    Point E(0, -2) is a vertex of square DEFG. After a 90* clockwise rotation of the square about the origin, which of the following is the location of E? A. (-2,0) B. (2,0) C. (2,2) D. (0,2) Point D(-3,5) is a vertex of triangle DEF. After rotation of the

  66. Physics

    rotating space station has radius 1380 m, measured from the center of rotation to the outer deck where the crew lives. What should the period of rotation be if the crew is to feel that they weigh one-half their Earth weight?

  67. Math, physics

    A rotating space station has radius 1380 m, measured from the center of rotation to the outer deck where the crew lives. What should the period of rotation be if the crew is to feel that they weigh one-half their Earth weight?

  68. ochem lab

    What is the expected observed rotation of a 9.1 x 10-5 M solution of compound X? Note: compound X has a specific rotation of [α]D20 = -49o and a molecular weight of 235.2 g/mol. In addition, the path length of the cell used to take the polarimetry

  69. algebra

    Point D(-3,5) is a vertex of triangle DEF. After rotation of the triangle about the origin D us located at (3,5). Which of the following was the rotation of the triangle? A. 90* (degrees) clockwise B. 90* Counterclockwise C. 180* D. 360*

  70. Physics (please help!!)

    The Crab pulsar (m=2.00x10^30 kg) is a neutron star located in the Crab Nebula. The rotation rate of the Crab pulsar is currently about 30.0 rotations per second, or 60.0pi rad/s. The rotation rate of the pulsar, however, is decreasing; each year, the

  71. Physics

    A large centrifuge is used to expose aspiring astronauts to accelerations similar to those experienced in rocket launches and atmospheric reentries. a) At what angular velocity is the centripetal acceleration 10 gs if the rider is 10.0 m from the center of

  72. Cosmology

    Which of the following statements is not true of spiral arms: they tend to trail the rotation of the galaxy they are sites of star formation they are amplified by resonances between the epicyclic frequencies of stars and the angular frequency of the spiral

  73. Math

    Find equations for a pair of lines M and N so R(sub n)compose R(sub m) is the given transformation. A. The translation that maps the origin onto (5,0) B. The rotation of 180o about a point (Xo, Yo) C. The rotation of 40o about the origin D. The translation

  74. Chemistry

    Suppose a student is measuring the optical rotation of a 1 M sample of (S)-(-)- Limonene. The path length is 13cm. What optical rotation should the student expect to measure?

  75. Physics

    Ronald Johnson, who is 80.0 kg, is running at 4.00 m/s when he suddenly jumps onto a stationary playground merry-go-round at a distance 1.50 m from the axis of rotation of the merry-go-round. Ronald Johnson is traveling tangentially to the edge of the

  76. Math

    what is the measure of the angle of rotation with respect to two lines that intersect to form a 25° angle?

  77. math;););)

    Apply the 57-degree counterclockwise rotation about the origin to the vectors [1, 0] and [0,1], then use the image vectors (written as columns) to form the coe cient matrix M for the rotation. Test M by calculating the products M[1] [0] and M[0] [1 ].

  78. Math

    [R] = [4/5 -3/5] and [S] = [-3/5 4/5] [-3/5 -4/5] and [4/5 3/5] are reflection matrices. Calculate [R·S] and verify that it can be identified as the matrix of rotation. Determine the angle of the rotation.

  79. geometry

    What is the measure of the angle of rotation with respect to two lines that intersect to form a 45° angle? What is the measure of angle of rotation and how do you go about finding it when given an angle? Thanks for explaining

  80. Math

    Given a rectangle is transformed using the rule (x,y)→(-x,-y),what transformation occurred?Rotation or reflection.If Rotation name the direction and degrees and if reflection name the line. I think it's Rotation 180 degrees.Is that correct?

  81. Organic Chemistry

    How am I supposed to do these questions? I'm completely lost. A 0.120 M solution of an enantiomerically pure chiral compound D has an observed rotation of 0.12° in a 1-dm sample container. The molar mass of the compound is 130.0 g/mol. (b) What is the

  82. Math

    Find a single matrix that defines a rotation of the plane through an angle of π/6 about the origin, while at the same time moves points to five times their original distance from the origin.

  83. math

    Find a single matrix that defines a rotation of the plane through an angle of π/6 about the origin, while at the same time moves points to five times their original distance from the origin.

  84. Math

    Can anyone please rephrase this. I really can't understand this term. Rotation symmetry: When a shape or design can be turned about its center of rotation, so it fits onto its outline MORE than once in a complete turn(360 degrees) I don't understand this.

  85. Math

    A triangle T with vertices A (2,4), B(6,2), and C(4,8) is mapped onto Triangle T’ with vertices A’(10,0), B’(8,-4) and C’(14,-2) by a rotation. Determine the center and angle of rotation that maps T onto T’.

  86. physics

    A ferris wheel makes one rotation in 15 minutes. Find your car's location and the angle of rotation after: 3 mins., 5 mins., 9 mins., 12 mins. The diameter of the wheel is 328 ft. and the height, with the base, is 369 ft.

  87. Math

    A ferris wheel makes one rotation in 15 minutes. Find your car's location and the angle of rotation after: 3 mins., 5 mins., 9 mins., 12 mins. The diameter of the wheel is 328 ft. and the height, with the base, is 369 ft.

  88. SCIENCE ASAP HELP PLEASE

    which of the following features make earth and venus similar to each other ? A . their size and mass b. their rates of rotation c. their atmospheres d. their directions of rotation****

  89. Science

    which of the following features make earth and venus similar to each other ? (1point ) A . their size and mass b. their rates of rotation c. their atmospheres d. their directions of rotation****

  90. Science

    which of the following features make earth and venus similar to each other ? (1point ) A . their size and mass b. their rates of rotation c. their atmospheres d. their directions of rotation****

  91. chemistry

    Calculate the specific rotation for Compound A, whose observed rotation was (+) 45.0 for a solution made from 0.400 g dissolved in 5 mL of chloroform solvent. The cell path length was 10 cm.

  92. Math

    Determine whether a regular decagon has reflection symmetry and/or rotational symmetry. If it has reflection symmetry, state the number of axes of symmetry. If it has rotation symmetry, state the angle of rotation. Explain how you determined your answers

  93. Physics- Someone Please Help!!!

    A luggage carousel at an airport has the form of a section of a large cone, steadily rotating about its vertical axis. Its metallic surface slopes downward toward the outside, making an angle of 21.0° with the horizontal. A 37.0 kg piece of luggage is

  94. Physics URGENT!!!

    A luggage carousel at an airport has the form of a section of a large cone, steadily rotating about its vertical axis. Its metallic surface slopes downward toward the outside, making an angle of 21.0° with the horizontal. A 37.0 kg piece of luggage is

  95. Math

    Given a rectangle is transformed using the rule (x,y)→(-x,-y),what transformation occurred?Rotation or reflection.If Rotation name the direction and degrees and if reflection name the line.

  96. Physics Urgent!!

    A day on Mars is 24.6 Earth hours long. A year on Mars is 687 Earth days long. How do the angular velocities of Mars’ rotation and orbit compare to the angular velocities of Earth’s rotation and orbit? w(M)/w(E)= and w(My)/w(Ey)= w is what I used to

  97. Trigonometry

    Find the angular speed in radians per sec. of the second hand on a clock. How long does it take for the second hand to make one rotation? And isn't one rotation 2pi radians? Let me know what you got as an answer.

  98. math

    After a triangle is rotated 180 degrees, its vertices are at (-4,1),(-1,4), and (-5,-8). What were the coordinates of the vertices before the rotation? I think the answer is (1,-4), (4,-1),(8,-5). In rotation, the coordinates get switched. All I just did

  99. Class 11th Physics

    I have read about Rotatory Motion it says "It is that motion in hwich body, which is not a point mass body is moving such that all its constituent particles move simultaneously along concentric circles, whose centres lie on a line, called axis of rotation

  100. analytic geometry

    how to convert the small rotation of axes into capital rotation of axes?

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