# 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

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

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

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

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

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

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

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

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*

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

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?