If $f(x)=\left|\begin{array}{ccc}-\sin x & 2 \sin 2 x & 4 \cos ^2 x \\ \cos x & 4 \sin ^2 x & 2 \sin 2 x \\ 0 & -\cos x & \sin x\end{array}\right|$, then $f\left(\frac{5 \pi}{4}\right)+f^{\prime}\left(\frac{5 \pi}{4}\right)=$

If $A+B=\left[\begin{array}{lll}2 & 1 & 2 \\ 1 & 2 & 0 \\ 0 & 2 & 2\end{array}\right], A B=\left[\begin{array}{lll}1 & 2 & 2 \\ 1 & 1 & 0 \\ 1 & 2 & 1\end{array}\right]$, then $A^2+B(A+B)=$

If $A, P, B$ are $3 \times 3$ matrices. If $|-B|=5,\left|B A^T\right|=15$, $\left|P^T A P\right|=-27$, then one of the values of $|P|$ is

If $A$ is a $3 \times 3$ matrix and $|A|=\frac{1}{2}$, then $\left|A^{-1}(\operatorname{Adj}(\operatorname{Adj} A))\right|^{-1}=$