Why can any affine transformaton be constructed from a sequence of rotations, translations, and scalings? A book on CG says:

... we can construct any affine transformation from a sequence of rotations, translations, and scalings.

But I don't know how to prove it.
Even in a particular case, I found it still hard. For example, how to construct 
a shear transformation from a sequence of rotations, translations, and scalings?
Can you please help? Thank you.
EDIT:  
Axis scalings may use different scaling factors for the axes.
Is there a matrix representation or proof for this?
For example, to show that a two-dimensional rotation can be decomposed into three shear transformation, we can write
$$
\begin{pmatrix}
\cos\alpha & \sin\alpha\\
-\sin\alpha & \cos\alpha
\end{pmatrix}
=
\begin{pmatrix}
1 & \tan\frac{\alpha}{2}\\
0 & 1
\end{pmatrix}
\begin{pmatrix}
1 & 0\\
-\sin\alpha & 1
\end{pmatrix}
\begin{pmatrix}
1 & \tan\frac{\alpha}{2}\\
0 & 1
\end{pmatrix}
$$

Perhaps using the singular value decomposition?
For the homogeneus case (linear transformation), we can always write
$y = A x = U D V^t x$ 
for any square matrix $A$ with positive determinant, were U and V are orthogonal and D is diagonal with positive real entries. U and V would the be the rotations and D the scaling.
Some (trivial?) details to polish: what if A has negative determinant, what is U and V are not pure rotations but also involve axis reflections.
It only remains add the indepent term to get the affine transformation ($y = Ax +b$) and that would be the translation.
