An ideal diatomic gas is made up of molecules that do not vibrate. Its volume compressed by a factor of 32,without any exchange of heat. If the initial and final pressures are P1 and P2,respectively,the ratio P1:P2,is:
Let $ X = \left\{ \begin{bmatrix} a & b \\ c & d \end{bmatrix} \middle| a, b, c, d \in \mathbb{R} \right\} $. If $ f: X \to \mathbb{R} $ is defined by $ f(A) = \det(A) $ for all $ A \in X $, then $ f $ is