It is worth noting that you can accomplish rotation with only a single trip to the Resize and Skew menu.
Paint applies the operations in the order: Resize, Skew Horizontal, Skew Vertical.
As a sequence of matrix transforms acting on a column vector, that is:
$$(\begin{bmatrix}1&0\\K_v&1\end{bmatrix}(\begin{bmatrix}1&K_h\\0&1\end{bmatrix}(\begin{bmatrix}S_h&0\\0&S_v\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix})))$$
Where $K_v$ and $K_h$ are the vertical and horizontal skew factors, and $S_v$ and $S_h$ are likewise the scale factors.
Because matrix multiplication is associative, let's remove the parentheses and multiply these transforms from left to right to give an equivilent single-matrix transform:
$$\begin{bmatrix}S_h&K_hS_v\\S_hK_v&K_hK_vS_v+S_v\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}$$
Setting this matrix equal to the rotation matrix, $\begin{bmatrix} \cos(θ) & \sin(θ) \\ -\sin(θ) & \cos(θ) \end{bmatrix}$, we get a system of equations which we can solve for our scale and skew factors:
$$S_h = \cos(θ)$$
$$K_h = \sin(θ)cos(θ)$$
$$S_v =1/\cos(θ)$$
$$K_v = -\tan(θ)$$
These variables describe factors in an affine transformation, but paint wants "% Resizing" and "degrees skew", so input:
$$\%R_h = 100*S_h=100*\cos(θ)$$
$$\%R_v = 100*S_v=100/\cos(θ)$$
$$DegSk_h = \arctan(K_h)=\arctan(\sin(θ)\cos(θ))$$
$$DegSk_v = \arctan(K_v) = \arctan(-\tan(θ))=-θ$$
As an operational note: Paint will automatically resize your selection after a skew if the skew transformation would put the selection outside of the canvas, so make sure you have plenty of room around your selection.