  A stellar system is dynamically hot when its kinetic energy is dominated by
random motion represented by the velocity dispersion $\sigma_{\rm hot} (M_*)$.
We use MaNGA data to obtain inner and outer dispersion of a galaxy,
$\sigma_{\rm in}$ and $\sigma_{\rm out}$, to characterize its dynamical status
and study its connection with star formation quenching and the growth of
supermassive black hole (SMBH). We divide galaxies into fully quenched (FQGs),
partially quenched (PQGs) and fully star-forming (FSGs) populations, and
identify quenched central cores (QCCs) in PQGs. The galaxy distribution in
$\sigma_{\rm in}/\sigma_{\rm hot}$-$\sigma_{\rm out}/\sigma_{\rm hot}$ diagram
is L-shaped, consisting of a horizontal sequence ($\sigma_{\rm out}/\sigma_{\rm
hot}\sim0$) and a vertical sequence ($\sigma_{\rm in}/\sigma_{\rm hot}\sim1$).
FQGs and QCCs are located at the top of vertical sequence, $\sigma_{\rm
out}/\sigma_{\rm hot}\sim1$, therefore they are dynamically hot over their
entire bodies. PQGs reside along vertical sequence, so they have hot center but
cold outskirt. FSGs are diverse and can be found in both sequences. Galaxy
structural properties, star formation and AGN activities make a transition
along horizontal sequence at $\log(\sigma_{\rm in}/\sigma_{\rm hot})\sim-0.3$,
and along vertical sequence at $\log(\sigma_{\rm out}/\sigma_{\rm
hot})\sim-0.3$. The fractions of optical AGNs and barred galaxies increase
rapidly in the first transition and decline rapidly in the second; radio
galaxies are located at the top of vertical sequence. Our results demonstrate
that star formation quenching and SMBH growth are effective only in dynamically
hot systems. A simple model along this line can reproduce the observed SMBH
scaling relations. We discuss how secular processes and strong interactions can
make a system dynamically hot, and lead to the SMBH growth and star formation
quenching.
