(a) The vector \(\mathbf v\) has a magnitude of 39 units and is in the same direction as \(\begin{pmatrix}-12\\5\end{pmatrix}\). Write \(\mathbf v\) in the form \(\begin{pmatrix}a\\b\end{pmatrix}\), where \(a\) and \(b\) are constants.

(b) Vectors \(\mathbf p\) and \(\mathbf q\) are such that \(\mathbf p=\begin{pmatrix}r+s\\r+6\end{pmatrix}\) and \(\mathbf q=\begin{pmatrix}5r+1\\2s-1\end{pmatrix}\), where \(r\) and \(s\) are constants. Given that \(2\mathbf p+3\mathbf q=\begin{pmatrix}0\\0\end{pmatrix}\), find the value of \(r\) and of \(s\).