Consider the following maps of polynomials \(S:\mathcal{P}\rightarrow\mathcal{P}\) and \(T:\mathcal{P}\rightarrow\mathcal{P}\) defined by

\[ S(h(x))= -h\left(x\right)^{2} - 2 \, h'\left(x\right) \hspace{1em} \text{and} \hspace{1em} T(h(x))= 3 \, h\left(4\right) + 4 \, h\left(x^{2}\right) \]

Explain why one these maps is a linear transformation and why the other map is not.