Rotating a parametric function

A student asked if it was possible to rotate a parametric function by an arbitrary angle theta using matrix multiplication: [math]\begin{bmatrix} \cos \theta &-\sin \theta\\ \sin \theta&\cos \theta \end{bmatrix} \begin{bmatrix} t\\ f(t) \end{bmatrix} = \begin{bmatrix} \cos \theta t-\sin \theta f(t)\\ \sin \theta t+\cos \theta f(t) \end{bmatrix}[/math] The answer of course is yes.