8. (10 points) Find the orthogonal matrix $Q$ in which $q_{11}>0$ and $q_{22}>0$, and the diagonal matrix $D$ such that

$\begin{bmatrix} x & y \end{bmatrix} Q D Q^T \begin{bmatrix} x \\ y \end{bmatrix} = 6x^2+24xy-y^2.$