I know that $SO(2)$ is generated by the set of matrices of the form
\begin{bmatrix} \cos(\theta) & \sin(\theta) \\ -\sin(\theta) & \cos(\theta) \end{bmatrix}
which can be used to find the matrices generated from various embeddings of $SO(2) \to SO(n)$. Is there a similar description for the matrix groups $SO(p,q)$?