= Solution
In the <computational basis>, write
$$
\rho=\frac12\begin{pmatrix}1+s_z&s_x-is_y\\s_x+is_y&1-s_z\end{pmatrix}.
$$
The <Kraus representation> of the <amplitude damping channel> gives
$$
\Lambda(\rho)=\begin{pmatrix}
\rho_{00}+p\rho_{11}&\sqrt{1-p}\,\rho_{01}\\
\sqrt{1-p}\,\rho_{10}&(1-p)\rho_{11}
\end{pmatrix}.
$$
Reading off its <Bloch vector> gives the <Bloch-vector map of amplitude damping>:
$$
\boxed{(s_x,s_y,s_z)\longmapsto
\left(\sqrt{1-p}\,s_x,\sqrt{1-p}\,s_y,p+(1-p)s_z\right).}
$$
Here $0\leq p\leq1$. The shift in $s_z$ shows that this <quantum channel> is not unital unless $p=0$; its fixed ground state lies at the north pole, rather than the center of the <Bloch sphere>.
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