What matrix represents the anticlockwise rotation through $\displaystyle \theta$...I think it perhaps might be $\displaystyle (\begin{array}{cc}cos\theta&-sin\theta\\sin\theta&cos\theta\end{array})$ but i'm not at all sure.
Many thanks
Yes that's right.
If you rotate (1,0) through x anticlockwise , you get the point (cos x, sin x) so that's your first column in the matrix
If you rotate (0,1) through x anticlockwise, you get (-sin x, cos x) so that is the second column in your matrix.
Best way to think of your transformation matrices is to consider the image of (1,0) and (0,1) and these form the columns of your matrix.