Find image of u under matrix transformation

Find the image of u under the matrix formation f:

f: $\displaystyle R^2-->R^2$ is a counterclockwise rotation through $\displaystyle 2/3$ pi raidans; u = the vector

-2

-3

I started by writing f(u)= cos(2/3 pi) -sin(2/3 pi)

sin(2/3 pi) cos(2/3 pi) * u

f(-2)= -1/2 ......-rad3/2....... -2 = (-1/2)(-2)+(-rad3/2)(-3)

(-3).... rad3/2.... -1/2... .*.. -3... (rad3/2)+(-1/2)(-3)

= (2+3rad3)/2 = 3.59808

= (3-2rad3)/2 = -.23205

My book does not explain how to do this at all. I was actally using the answer to another problem in a solutions manual as a guide. Can anyone confirm if I did this problem right? Thanks!

P.S. I used all the periods to try and space the matrix and vector out since I'm not sure how to type it out correctly.

My calculation of second coordinate

http://www.mathhelpforum.com/math-he...377d09f3-1.gif. If http://www.mathhelpforum.com/math-he...63711069-1.gif

I replaced the thetas with (2/3 pi) radians and to get the second coordinate, I calcuated sin(2/3 pi)(-2)+cos(2/3 pi)(-3)=(radical3)/2)*(-2)+(-1/2)(-3)=[3-2(radical3)]/2= -.23205