Friday

May 22, 2015

May 22, 2015

Number of results: 61,982

**Vectprs and Scalars**

Why are some of these scalars and others are vectors? What's the difference and how can you tell? 1. a dot (b x c) 2. (a dot b) x (b dot c) 3. (a + b) dot c 4. a x (b dot c) 5. (a x b) dot (b x c) 6. (a + b) x c 7. a dot (b dot c) 8. (a x b) + (b x c) 9. (a x b) - c 10. a x (b...
*February 9, 2015 by annonymous*

**Dynamics**

Which one of the following statement is correct Multiple choice question a)Energy and work are scalars b)Force and work are vectors c)Energy, momentum and velocity are vectors d)Force, momentus and velocity are scalars
*August 4, 2012 by Rajan*

**Physics**

please check these: which of the following is an example of a vector quantity? a. velocity b. temperature c. volume d. mass i picked A identify as vecor or scalar 1. speed of a snail---vector 2. the time it takes to run a mile-scal 3. the free-fall accleration---vector 3. ...
*January 31, 2009 by y912f*

**dyanamics**

Which one of the following statements is correct? (a) Energy and work are scalars (b) Force and work are vectors (c) Energy, momentum and velocity are vectors (d) Force, momentum and velocity are scalars
*August 3, 2012 by raja*

**Vectors**

Vectors "v" and "w" are given by v = 5i - 2j and w = i + 3j. Find scalars r and s such that r ( v - w) = ( r + s )i - 20j.
*April 26, 2012 by Cameron*

**physics: scalars/vectors**

Please check. 1. Which of the following quantities are scalars, and which are vectors? a. the acceleration of a plane as it takes off- VECTOR b. the number of passengers on the plane- SCALAR c. the duration of the flight- SCALAR d. the displacement of the flight- VECTOR e. the...
*September 17, 2006 by Anonymous*

**math**

The vectors u, v are given by u = 3i + 5j, v = i - 2j. Find scalars a, b such that a(u + v) = 8i + (b - 2)j
*May 16, 2010 by Michael*

**math**

The vectors u, v are given by u = 3i + 5j, v = i - 2j. Find scalars a, b such that a(u + v) = 8i + (b - 2)j
*May 16, 2010 by Michael*

**linear algebra**

Show that a subset W of a vector space V is a subspace of V if and only if the following condition holds: If u and v are any vectors in W and a and b are any scalars, then au + bv is in W.
*July 11, 2007 by chris*

**Physics (vectors)**

Given vectors A= (Axi + Ayj), B= (Byj+Bzk) and C= (Cyj + Czk). a) find the triple product of these vectors defined by A dot (BxC) in terms of the vector components. I get 0 as the answer. b) is the result found in a) a scalar of a vector? since I had to multiply finally by the...
*January 23, 2007 by steve*

**physics**

Matt runs away from Ashley. Matt runs 40 m north and 30 m west. What is the minimum distance Ashley must run to catch Matt? Draw the image and label the vectors and scalars.
*October 4, 2012 by Lauren*

**algebra**

Is this set a subspace of R3 or not? Explain why or why not. Span{[1 2 1],[-1 1 3]} I've tried to do a three variable three unknown equation to solve for the scalars for each of the vectors but when doing it got very wrong numbers.
*September 22, 2014 by Jackk*

**physics 4**

help me in this topicsmass vol.relationship,graphs and itinterpretation,vectors and scalars help me more to understand this topics the tools in physics,measurement,vectors and scales It is quite impossible to divine what you dont understand. We can easily critique your ...
*August 6, 2005 by pamea*

**physics**

Can you help me with this one also? I know how to do it with 3 vectors but I can't seem to draw it with 4 vectors. The magnitudes of the four displacement vectors shown in the drawing are A=16.0 m, B=11.0 m, C=12.0 m, and D=26.0 m. Determine the (1) magnitude and (2) ...
*January 23, 2011 by Brittany*

**Physics**

2 vectors have same magnitude.The magnitude of the resultant vector of these 2 vectors are same as either of both vectors.What is the angle between 2 vectors?
*November 21, 2014 by Tangy*

**Vectors/Scalars?**

is (u dot v)dot (a dot c) a scalar quantity or vector quantity? What's the difference? (I'm thinking scalar since it has no direction and it only has magnitude.)
*February 8, 2015 by annonymous*

**physics multiplying vectors**

n the product F = qv · B , take q = 4, = 2.0i + 4.0j + 6.0k and = 136i -176j + 72k. What then is in unit-vector notation if Bx = By? ~~may i get some assistance in this problem? so far.. i tried this.. 136i-176j+72k = 4(2.0i+4.0j+6.0k)(B) 136i-176j+72k = (8i+16j+24k)(B) [(136i...
*March 29, 2007 by sam*

**math**

given that vectors(p+2q) and (5p-4q) are orthogonal,if vectors p and q are the unit vectors,find the dot product of vectors p and q?
*January 2, 2013 by bhawani*

**Physics Vectors**

two vectors A and B have magnitude such that A>B. We do not know the directions of the vectors. however we can say that the magnitude of the sum A+B must be between? a) B and 2A b)A and A+B c) A-B and A+B d) A-B and A e) B and A+B
*September 27, 2012 by cody*

**math**

given that vectors(p+2q) and (5p-4q) are orthogonal,if vectors p and q are the unit vectors,find the product of vectors p and q?
*January 1, 2013 by bhawani*

**Physics**

I don't know if my answers are right. D: 1)Why is a time interval always positive? I'm not really sure but I wrote down something with vectors and scalars. 2)If the average acceleration of a car is zero in a given time interval, what can you tell about the displacement of the ...
*October 1, 2014 by Selena*

**Physic Worksheets?**

Hi! I have a few tests coming up and I need some practice Physics worksheet/tests. I have already done the worksheets and previous tests, but I still need more practice. Does anyone know a site that I can get some practise problems? Doing a google search only leads to higher ...
*January 6, 2015 by Lucina*

**physics**

Which of :acceleration,age,speed,temperature,and velocity are vector quantities? Are any of them scalars?
*June 14, 2011 by alexa*

**physics**

Given the vectors = (19 cm, -7 cm) in green and = (-23 cm, 9 cm) in blue shown on the grid below, calculate the magnitude of the vectors described below and select the correct sketch for each from the choices below. The tail-to-head method is used to represent the operations ...
*October 15, 2013 by butcha*

**physics-vectors**

If the magnitude of the sum of two vectors is greater than the magnitude of either vector, then: If the magnitude of the sum of two vectors is less than the magnitude of either vector, then: a. the scaler product of the vectors must be negative b. the scaler product of the ...
*August 6, 2007 by mekeke*

**physics**

The vectors sum of two vectors of magnitude 10units and 15units can never be
*July 4, 2014 by raghavendra*

**Math - Algebraic Vectors**

Given the vectors: u = [3, 0] v = [-1, 2] a) Express the vector w = [2, 8] as a linear combination of vectors u and v. How do I do this?
*February 13, 2008 by Anonymous*

**math**

two vectors are defined as a=2i+xj and b=i-4j. find value of x if a) the vectors are parallel b) the vectors are perpendicular
*November 21, 2010 by karla*

**math**

two vectors are defined as a=2i+xj and b=i-4j. find value of x if a) the vectors are parallel b) the vectors are perpendicular
*November 21, 2010 by karla*

**PreCalculus**

Given vectors u=7i + 3j and v = -4i + 3j, find 5u-4v in terms of unit vectors. I am just beginning the study of vectors and have this problem. Could someone help? Thanks.
*January 29, 2009 by Joanie*

**Physics**

Find the scalar product of the vectors ai+bj and bi-aj . Where a and b are arbitrary constants. What's the angle between the two vectors?
*May 30, 2013 by Jacob*

**physics**

Find the vectors.sum of ihe three vectors A=-3i-2j+7k, B=i+3j+k, C=-k
*February 4, 2013 by baron*

**Physics**

Given the displacement vectors A = (7.00 - 1.00 + 3.00 ) m and B = (6.00 + 5.00 - 3.00 ) m, find the magnitudes of the following vectors and express each in terms of its rectangular components. (a) C = A - B (b) D = 3A + B
*September 26, 2012 by Abraham*

**math**

if vectors a+b+c=0 and modulus of the vectors a, b and c are 3 ,5 and 7 respectively. find the angle between the vectors a and b.
*January 5, 2013 by raja*

**Calculus**

Name two sets of vectors that could be used to span a set in R^3. Show how the vectors (-1,2,0) and (3,4,0) could each be written as a linear combination of the vectors you have chosen.
*April 28, 2010 by Jackiee*

**Science**

2 vectors have same magnitude.The magnitude of the resultant vectors is same as either of both vectors.What is the angle between 2 vectors?
*November 21, 2014 by Tangy*

**Physics**

The sum & difference of two non-zero vectors Ä & B are equal in magnitude.what can you conclude about these vectors?why?
*November 25, 2012 by Minte*

**Calculus and Vectors**

THE VECTORS a - 5b AND a-b ARE PERPENDICULAR. IF a AND b ARE UNIT VECTORS, THEN DETERMINE a dot b
*May 11, 2013 by Johnny*

**physics**

The magnitudes of the four displacement vectors shown in the drawing are A = 15.0 m, B = 11.0 m, C = 12.0 m, and D = 21.0 m. Determine the magnitude and directional angle for the resultant that occurs when these vectors are added together.
*January 20, 2012 by Anonymous*

**physics**

Consider two vectors ~ A and ~ B and their re- sultant ~ A + ~ B . The magnitudes of the vectors ~ A and ~ B are, respectively, 13 . 2 and 6 . 1 and they act at 110 ◦ to each other.Find the magnitude of the resultant vector ~ A + ~ B .
*January 19, 2015 by allan*

**Physics**

Vectors and Scalars Graph 1. determine the total distance traveled and the displacement made. A. 5.0 km 15 degrees east of north B. 5.0 km 20 degrees east of south C. 5.0 km east D. 5.0 km 30 degrees south of west E. 5.0 km 20 degrees east of south F. 5.0 km 40 degrees north ...
*July 12, 2012 by Vicky*

**Physics**

If a&b are vectors such that a+3b=-3i+j & a-b=i-2j then find vectors a&b.
*November 16, 2011 by Emily*

**Calulas and VECTORS**

THE VECTORS a - 5b AND a-b ARE PERPENDICULAR. IF a AND b ARE UNIT VECTORS, THEN DETERMINE a * b
*May 19, 2010 by z...........................*

**Calculus and vectors**

Please, help I don't understand vectors T.T 1. In the prism, assume all dimensions have different lengths, state the following: a) state 3 equal vectors to DC⃗ b) state 4 opposite vectors to BC⃗ ------------------------------------- Here is the prism below, imgur ...
*March 18, 2012 by Melissa*

**vectors**

Determine whether each statement is true or false. Provide a brief justification. a. Two lines with parallel direction vectors willnot intersect. b. Two linesthat are perpendicularin R3 willhave perpendicular direction vectors. c. Two linesthat havenon-paralleldirection ...
*June 9, 2010 by Alicia*

**physical science**

The resultant vector of two particular displacement vectors dose not equal the sum of the magnitudes of the individual vectors. Describe the directions of the two vectors.
*May 2, 2011 by Becky*

**Calculus and vectors**

A parallelogram is formed by R^3 by the vectors PA=(3,2,-3) and PB=(4,1,5). The point P=(0,2,3). a) what are the location of the vertices? b) what are the vectors representing the diagonals? c) what are the length of the diagonals?
*March 23, 2012 by Melinda*

**physics**

A football player runs the pattern given in the drawing by the three displacement vectors A, B, and C. The magnitudes of these vectors are A = 5.0 m, B= 15 m, and C = 18 m. Using the component method, find the magnitude and direction è of the resultant vector
*February 8, 2013 by james*

**12th grade**

prove that normal to plane containing 3 points whose position vectors are a vector,b vector,c vectorlies in direction addition of cross product of vectors b and c and cross product of vectors c and a and cross product of vectors a and b
*September 22, 2009 by parth*

**Physics**

Two vectors are at right angle to each other as shown. Find the resultant vector (the sum of the two vectors).
*March 4, 2012 by Mina*

**physics**

two vectors A and B have magnitude such that A>B. We do not know the directions of the vectors. however we can say that the magnitude of the sum A+B must be between? a) B and 2A b)A and A+B c) A-B and A+B d) A-B and A e) B and A+B
*September 27, 2012 by Kylie*

**Math**

Let u= (2,1,0,1,-1) and v=(-2, 3, 1, 0,2). Find scalars a and b so that au-bv=(-8,8,3,-1,7)
*April 6, 2012 by Lynn*

**Vectors**

THE VECTORS a - 5b AND a-b ARE PERPENDICULAR. IF a AND b ARE UNIT VECTORS, THEN DETERMINE a * b
*May 11, 2013 by Johnny*

**Physics**

How does the resultant of two vectors change as the angle between the two vectors increase?
*September 30, 2011 by Lala*

**Physics**

How does the resultant of two vectors change as the angle between the two vectors increase?
*October 2, 2011 by Lala*

**Physics Help!!!!**

Describe what it means (describe the motion) if the acceleration vector has the same direction as the velocity vectors, and what it means if the acceleration vector has the opposite direction as the velocity vectors. Consider all four possibilities and explain what would ...
*September 5, 2014 by Layla*

**Physics Help!!!!**

Describe what it means (describe the motion) if the acceleration vector has the same direction as the velocity vectors, and what it means if the acceleration vector has the opposite direction as the velocity vectors. Consider all four possibilities and explain what would ...
*September 6, 2014 by Layla*

**vectors**

ok theres a graph. its like this. basically theres a ray coming from the origin going up and left diagonally at about a 30 degree angle. the question says "for the following vectors draw the component vectors along the x and y axis". what do i do?!
*August 5, 2009 by jawn*

**Physics**

A football player runs the pattern given in the drawing by the three displacement vectors , , and . The magnitudes of these vectors are A = 6.00 m, B = 13.0 m, and C = 15.0 m. Using the component method, find the (a) magnitude and (b)direction of the resultant vector + + . ...
*July 9, 2011 by Kristi*

**Physics**

What is the resultant of two displacement vectors having the same direction? a. The resultant is the sum of the two displacements having the same direction as the original vectors. b. The resultant is the difference of the two displacements having the same direction as the ...
*February 5, 2008 by Shenay*

**physics**

the vectors sum of two vectors of magnitudes 10 units and 15 units can never be?
*July 5, 2014 by raghavendra*

**Physics**

A student accurately uses the method for combining vectors. The two vectors she combines have magnitudes of 55 and 25 units. The answer that she gets is either 85, 20, or 55. Pick the correct answer, and explain.
*September 27, 2010 by Anonymous*

**Physics**

A football player runs the pattern given in the drawing by the three displacement vectors A ,B ,C and . The magnitudes of these vectors are A = 4.00 m, B = 17.0 m, and C = 19.0 m. Using the component method, find the (a) magnitude and (b)direction of the resultant vector A + B...
*July 14, 2011 by Kelli*

**Physics**

1) The vector sum of three vectors gives a resultant equal to zero. what can you say about the vectors? 2) Vector is 3.00 units in length and points along the positive x-axis. Vector is 4.00 units in length and points along the negative y-axis.Use graphical methods to find the...
*November 19, 2009 by Aman*

**Physics (vectors)**

Could you please help me with this exercise? Thanks. Adding and substracting vectors Solve for the unknown variables: (a) (a, b) + (3, 0) = (6, 7) (b) (11, c) + (d, 5) = (-12, −3) (c) (5, 5) + (e, 4) = (2, f) (d) (-1, −3) − (5, g) = (h, 2)
*February 13, 2013 by Kathy*

**Physics (vectors)**

Could you please help me with this exercise? Thanks. Adding and substracting vectors Solve for the unknown variables: (a) (a, b) + (3, 0) = (6, 7) (b) (11, c) + (d, 5) = (-12, −3) (c) (5, 5) + (e, 4) = (2, f) (d) (-1, −3) − (5, g) = (h, 2)
*February 13, 2013 by Kathy*

**Maths-Vectors Help!**

Please can you help me as I have just been introduced to your Help Forum: Determine whether the vectors u, v and w given below are linearly independent or dependent where u, v and w are non-colliner vectors such that u=2a-3b+c , v=3a-5b+2c and w=4a-5b+c. thanks. Use exactly ...
*April 16, 2007 by Charles*

**vectors**

If two vectors u and v fit the equation (u − v) • (u − v) = u•u+v•v, how must these vectors u and v be related? What familiar theorem does this equation represent?
*April 12, 2010 by sally*

**physics**

The problem concern the position vectors r1=2.43mi-4.74mj and r2=-3.02mi+0.85mj. Find the angle between the two vectors. Hint: Find the angle each makes with the +x-axis.
*June 12, 2011 by Wykeena*

**physics**

The problem concern the position vectors r1=2.43mi-4.74mj and r2=-3.02mi+0.85mj. Find the angle between the two vectors. Hint: Find the angle each makes with the +x-axis.
*June 12, 2011 by Wykeena*

**physics**

The problem concern the position vectors r1=2.43mi-4.74mj and r2=-3.02mi+0.85mj. Find the angle between the two vectors. Hint: Find the angle each makes with the +x-axis.
*June 12, 2011 by Wykeena*

**linear algebra**

which of the following sets of vectors span R^3? a.){(1, -1, 2), (0, 1, 1)} b.) {1, 2, -1), (6, ,3, 0), (4, -1, 2), (2, -5, 4)} c.) {(2, 2, 3), (-1, -2, 1), (0, 1, 0)} d.) {(1, 0, 0), (0, 1, 0), (0, 0, 1), (1, 1, 1)} can someone show the steps to check for one of them and i ...
*July 19, 2007 by chris*

**Physics**

2. We have two vectors that line in the x-y plane. If we take the cross-product of those two vectors we know that a. the magnitude of the cross-product will always be equal to the product of the magnitudes of the two vectors. b. the magnitude of the cross-product will always ...
*December 27, 2011 by Sarah*

**physics [vectors]**

The concept i get, but somehow i just can't execute this problem, please help me! You are given vectors A = 5.5 6.2 and B = - 3.7 7.4 . A third vector C lies in the xy-plane. Vector C is perpendicular to vector A and the scalar product of C with B is 19.0. I need x and y ...
*August 30, 2009 by lina*

**physics**

Vector A is given by A = c x + 6 y, and vector B is given by B = 4.8 x - 16.2 y, where x and y are the x and y unit vectors. What does c need to be such that these two vectors are perpendicular?
*October 28, 2010 by sam*

**physics**

Suppose vector A=3i-2j, B= -i-4j and vector C are three vectors in xy plane with the property that vectors A+B-C. What is the unit vector along vector C?
*January 28, 2012 by Abdela said yimer*

**Physics**

Multiple Concept Example 9 provides background pertinent to this problem. The magnitudes of the four displacement vectors shown in the drawing are A = 16.0 m, B = 12.0 m, C = 13.0 m, and D = 23.0 m. Determine the (a) magnitude and (b) direction for the resultant that occurs ...
*May 29, 2012 by Sara*

**physics**

Multiple Concept Example 9 provides background pertinent to this problem. The magnitudes of the four displacement vectors shown in the drawing are A = 15.0 m, B = 10.0 m, C = 12.0 m, and D = 29.0 m. Determine the (a) magnitude and (b) direction for the resultant that occurs ...
*March 10, 2014 by marah*

**physics**

Three vectors are shown in Fig. 3-32 (A = 62.0 , B = 58.0°). Their magnitudes are given in arbitrary units. Determine the sum of the three vectors. (a) Give the resultant in terms of components. Rx = Ry = (b) What is the magnitude of the resultant? What is the resultant's ...
*September 30, 2012 by michael*

**physics**

Three vectors are shown in Fig. 3-32 (A = 60.0 , B = 56.0°). Their magnitudes are given in arbitrary units. Determine the sum of the three vectors. (a) Give the resultant in terms of components. (b) What is the magnitude of the resultant? What is the resultant's angle above ...
*September 30, 2012 by joe*

**Physics**

Find the magnitude and direction of the resultant R of the three vectors shown in figure 1.3. The vectors have the following magnitudes: A=5.0, B=7.9, and C=8.0. Express the direction of the vector sum by specifying the angle it makes with the positive x-axis, with the ...
*October 10, 2014 by Anonymous*

**Math vectors**

For which of the following conditions will the cross product of two vectors be zero? a) If the angle between them is 90°. b) If the angle between them is 0°. c) If the angle between them is 45°. d) If the vectors have the same magnitude.
*February 26, 2015 by Sheliza*

**college Algebra/Linear Algebra**

Find a Basis for each of these substances of R^4 (a) All vectors whose components are equal (b) All vectors whose component add to zero (c) All vectors that are perpendicular to (1,1,0,0) and (1,0,11) (d) The column space (In R^2) and nullspace(In R^5) of U=[1 0 1 0 1] [0 1 0 ...
*November 3, 2010 by traxx*

**perpendicular vectors**

Find two unit vectors each of which is perpendicular to vectors (1, 1, 0) and (1,0,1) What I did: a x b = (1, -1, -1) |axb|=square toot 3 correct answer is +/- (1/√3 - 1/√3 - 1/√3) or =+/- 1/√3 (1, -1, -1)
*February 11, 2015 by annonymous*

**Physics (vectors)**

Please help me with this question about vectors. Thanks. If you are given a graph with a vector starting at the point (1,-1)and the arrow goes to the point (0,-4). What is the vector in rectangular coordinate? I answered (0,-3), but the coordinate for x is wrong and I can't ...
*February 13, 2013 by Kathy*

**Physics**

A football player runs the pattern given in the drawing by the three displacement vectors A, B, and C. The magnitudes of these vectors are A = 5 m, B = 13.0 m, and C = 16.0 m. Using the component method, find the magnitude and direction è of the resultant vector A + B + C. (...
*August 18, 2010 by yoyoma*

**physics**

A sailboat race course consists of four legs, defined by the displacement vectors , , , and , as the drawing indicates. The magnitudes of the first three vectors are A = 2.80 km, B = 4.70 km, and C = 4.50 km. The finish line of the course coincides with the starting line. ...
*June 17, 2014 by Anonymous*

**Physics**

2 displacement vectors of 15 meters and 10 meters are combined. a.Find the magnitude of the minimum possible resultant and the angle between the vectors. b. Find the magnitude of the maximum possible resultant and the angle between the vectors.
*September 16, 2007 by Bailey*

**physics**

The magnitude of the scalar product of vectors A and B is three times as large as the magnitude of the vector product of the same two vectors. If they were placed tail-to-tail in space, A and B would form an angle of approximately how much?
*December 8, 2010 by Edith*

**AP Physics**

there are two vectors in quadrant three one with a magnitude of 31.0N and has a direction of 117degrees in the negative direction from the x axis the other has an unknown magnitude and unkown theta in the positive direction starting from 90 degrees Find the scalar product of ...
*November 21, 2010 by Sierra*

**math**

Two vectors have magnitudes of 3 units and 8 units respectively. The resultant of these two vectors has a magnitude of 8 units. What is the angle between these two vectors?
*March 1, 2013 by dave*

**PHYSICS VECTORS**

1. The problem statement, all variables and given/known data Find the vector product of Vector A cross Vector B(expressed in unit vectors) of the two vectors. What is the magnitude of the vector product? 2. Relevant equations Vector A= 5.00i + 2.00j Vector B= 3.00i - 1.00j 3...
*September 17, 2009 by RAYMOND*

**Grade 12 Math**

if a and b are unit vectors, and magnitude of vectors a +b = sq. root of 3, determine (2a-5b) dot (b+3a).
*May 8, 2014 by Melissa*

**physics**

Four vectors, each of magnitude 89 m, lie along the sides of a parallelogram. The angle between vector A and B is 77◦. A 89 m C 89 m B 89 m D 89 m What is the magnitude of the vector sum of the four vectors? Answer in units of m I got 346.8757431m, but that's not right...
*September 1, 2011 by Jane*

**Math**

Prove that vectors u, v and w are coplanar if and only if vectors u, v and w are linearly dependent.
*April 18, 2008 by Tess*

**Vectors**

If vector a and b are unit vectors, and |a+b|= root3, determine (2a-5b) dot product(b+3a)
*May 19, 2010 by Shawn*

**Calculus/Vectors**

Calculate the area of the parallelogram with sides consisting of the vectors: a = (1,2,-2) b = (-1,3,0)
*May 17, 2011 by Anonymous*

**Vectors/Calc**

Calculate the area of the parallelogram with sides consisting of the vectors: a = (1,2,-2) b = (-1,3,0)
*May 17, 2011 by Anonymous*

**Calculus and vectors**

Do the vectors (2,0,1),(-2,0,0) and (2,3,0) lie on the same plane? Explain your reasoning.
*March 26, 2012 by Melinda*

**Vectors**

Vectors a and b have magnitudes 2 and 3, respectively. If one of them is 50degrees, find the vector 5a-2b and state its magnitude.
*June 15, 2008 by Sam*