Where does the rotation matrix come from?

Question

I looked through many different books, but none of them explain how they derive the matrix below. They just state it as is and move on. Can you explain, please.

$ \begin{bmatrix} R(\vec e_1), R(\vec e_1) \end{bmatrix} = \begin{bmatrix} cos x & - sinx \\ sinx & cosx \end{bmatrix}$

Answer 1

It comes from consideration of the transformed positions of the unit vectors