You got the first coordinate of the image of correct, but I think there is an error with the second. I got (roughly) -3.23.

In general, the matrix of transformation for a counterclockwise rotation of (about the origin) in is . If , and you want to find the image of under this transformation all you have to do is multiply matrix*vector. Looks like you know this already, but I'm not sure where your matrix came from and thought that a clean presentation would be enough to clear-up whatever arithmetic errors may have occurred.