Solve {l}{A_{x}=a_{x}cos(θ)-a_{y}sin(θ)}{A_{y}=a_{x}sin(θ)+a_{y}cos(θ)}

$$\left. \begin{array} { l } { A _ { x } = a _ { x } \cos ( \theta ) - a _ { y } \sin ( \theta ) } \\ { A _ { y } = a _ { x } \sin ( \theta ) + a _ { y } \cos ( \theta ) } \end{array} \right.$$

Solve for A_x, a_x, θ, a_y, A_y

$$\theta \in \mathrm{R}$$

$$A_{x}=a_{x}\cos(\theta )-a_{y}\sin(\theta )$$

$$a_{x}\in \mathrm{R}$$

$$a_{y}\in \mathrm{R}$$

$$A_{y}=a_{x}\sin(\theta )+a_{y}\cos(\theta )$$