## clockwise direction

Find the matrix A of the linear transformation T from $$R^2$$ to $$R^2$$ that rotates any vector through an angle of $$135^o$$ in the clockwise direction.

my book does not talk about how to answer this question. I've seen a change in 90 degrees, but I dont know how to do a 135 degree.
 PhysOrg.com science news on PhysOrg.com >> City-life changes blackbird personalities, study shows>> Origins of 'The Hoff' crab revealed (w/ Video)>> Older males make better fathers: Mature male beetles work harder, care less about female infidelity
 Look at the idea how to do it 90 degrees, the same idea applies.
 I guessed on how to get the 90 degree one, since it was mulitple choice. so i dont actually know the process, could someone explain it to me?

Recognitions:
Homework Help

## clockwise direction

You can look at what the transformation does to the standard basis, what is T(1,0) and T(0,1)? These determine the 1st and 2nd columns of A respectively and can be found using a little trig. More generally you can find a rotation by any angle this way.
 how can this be found with trig? i dont even know how linear transformations have to do with rotations, not sure at all what is going on because this hw questions came out of the blue
 Recognitions: Homework Help Science Advisor I mean you can find T(1,0) and T(0,1) in terms of sin's and cos's of your angle. Can you find T(1,0) and T(0,1)? Drawing a picture will help. A rotation about the origin is a linear transformation.
 so T(1,0) represents sin(90) and T(0,1) = cos(90)?

Recognitions:
Homework Help
 it's in the thrid quadrant. it makes a 45 degree angle with the x axis. so the x is $$-\frac{\sqrt{2}}{2}$$ which would be the same for the y