Solving Rotation Matrices Urgently: cos(pi/4) -sin(pi/4) sin(pi/4) cos(pi/4)

AI Thread Summary
The discussion focuses on understanding rotation matrices, specifically the matrix for a 45-degree rotation represented by cos(pi/4) -sin(pi/4) and sin(pi/4) cos(pi/4). The user expresses confusion about a follow-up question related to a matrix that not only rotates but also doubles the length of a vector. A contributor clarifies that the provided matrix is indeed a rotation matrix, emphasizing its property of preserving vector length. The main goal is to find a matrix that achieves both rotation and length doubling. The conversation highlights the importance of distinguishing between rotation and scaling in matrix transformations.
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[URGENT] Rotation Matrices

Homework Statement



http://e.imagehost.org/0661/Screen_shot_2010-03-09_at_12_37_44_AM.png

Homework Equations



Rotation Matrix:
cos(theta) -sin(theta)
sin(theta) cos(theta)

The Attempt at a Solution



I understand 2a:

cos(pi/4) -sin(pi/4)
sin(pi/4) cos(pi/4)

But I am not sure what 2b is looking for. Please help?

Thank you in advance for your help!
 
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The matrix you wrote is a rotation matrix, which rotates a vector but leaves its length unchanged. You need a matrix which doubles the length as well. Try to find such one. ehild
 
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