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(1 point) a. Find the Laplace transform $F(s)=\mathcal{L}\{f(t)\}$ of the function $f(t)=\sin ^{2}(w t)$, defined on the interval $t \geq 0$. \[ F(s)=\mathcal{L}\left\{\sin ^{2}(w t)\right\}= \] \# help (formulas) Hint: Use a double-angle trigonometric identity. b. For what values of $s$ does the Laplace transform exist? \# help (inequalities)

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