how do I do the following:
Consider the matrix $\begin{bmatrix} \cos x & -\sin x\\ \sin x & \cos x \end{bmatrix}$ and the vector $\begin{bmatrix} \cos y\\ \sin y \end{bmatrix}$. Show that the product of the $2\times 2$ matrix with $2\times 1$ matrix $\begin{bmatrix} \cos(x+y)\\ \sin(x+y) \end{bmatrix}$ graphically, by sketching.
I can show this using trig identities, but I am not sure how to graph the $2\times 1$ trig vector in first place, let alone explain the rest of the question graphically. All the help very much appreciated!