Consider a linear transformation $T(x)=Ax$ from ${\mathbb R}^2$ to ${\mathbb R}^2$. Suppose for two vectors $\vec{v}_1$ and $\vec{v}_2$ in ${\mathbb R}^2$ we have $T(\vec{v}_1)=3 \vec{v}_2$ and $T(\vec{v}_2)=-5 \vec{v}_1$. Find the determinant of the matrix $A$.

$\det(A) =$