Consider the figure above. Force $f$ is measured as $\left[\begin{array}{c}1\\-1\\\end{array}\right]$ N in the u,v coordinate frame. What is Force $f$ in the x,y coordinate frame?

A. $f= \begin{bmatrix} \sin\beta \\ \cos\beta\end{bmatrix}\, N$
B. $f= \begin{bmatrix} \cos\beta \\ \sin\beta\end{bmatrix}\, N$
C. $f= \begin{bmatrix} \cos\beta + \sin\beta \\ \sin\beta - \cos\beta\end{bmatrix}\, N$
D. $f= \begin{bmatrix} \cos\beta - \sin\beta \\ \sin\beta + \cos\beta\end{bmatrix}\, N$
E. $f= \sqrt{2}\begin{bmatrix} \sin\beta \\ \cos\beta\end{bmatrix}\, N$