= Solution
A <blackbody> absorbs all incident radiation and, in thermal equilibrium, emits the <Planck law> spectrum with integrated flux $\sigma T^4$. Earth reflects some incoming sunlight, while its surface and atmosphere absorb and emit selectively with wavelength. With solar irradiance $S_0$ and <Bond albedo> A, the equilibrium <planetary effective radiating temperature> is
$$
\boxed{\sigma T_{\rm eff}^4=\frac{(1-A)S_0}{4}.}
$$
Reflection lowers this temperature relative to the zero-albedo value. The <greenhouse effect> makes the surface warmer than the effective emitting temperature: in a simple diagnostic $\mathrm{OLR}=\epsilon_{\rm eff}\sigma T_s^4$, $T_{\rm eff}=\epsilon_{\rm eff}^{1/4}T_s$. This effective emissivity summarizes atmospheric transfer, not a universal material constant. At fixed absorbed sunlight, greenhouse warming does not require a different equilibrium outgoing flux. <Climate and Earth's Energy Budget by NASA Earth Observatory>[Absorbed/reflected sunlight and effective radiating versus surface temperature]{ref}
The stated \b[$0.9\,\mathrm{W\,m^{-2}}$ is positive net energy uptake], not necessarily the imposed <radiative forcing> itself. A linear <climate forcing-response energy balance> is
$$
\boxed{N=F-\lambda\Delta T=C\frac{d\Delta T}{dt},\qquad \lambda>0.}
$$
Here F is the perturbing forcing, $\lambda\Delta T$ is the net stabilizing radiative response and C is an effective areal heat capacity. The residual heats the Earth system, mainly through ocean heat uptake, with additional storage and melting. Finite heat capacity and ocean exchange delay equilibration. The imbalance alone determines neither F, the warming rate without C, nor the eventual equilibrium warming $F/\lambda$. Feedbacks change the response coefficient. The given number is treated as the examination's premise, not a present-day observational estimate. <The Earth's Energy Budget, Climate Feedbacks, and Climate Sensitivity by Piers Forster and others>[§7.4.1 andBox7.1, forcing–response budget; sign convention here uses positive damping lambda]{ref}
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