Finding what a rotation matrix transformation does to a vector

[rrm74001]

[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!

 

[ehild]

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