We set $A_2 = \operatorname{diag}(9, 5, 4)$ and $C = \left\{ U \in \mathcal{M}_{n,1}(\mathbb{R}) \mid U^\top U = 1 \right\}$. In this question only, we assume that $Y$ is a random variable with values in $\mathcal{M}_{3,1}(\mathbb{R})$ such that $\Sigma_Y = A_2$. Determine the maximum of $q_Y$ on $C$, where $q_Y(U) = \mathbb{V}(U^\top Y)$.