An opaque horizontal flat plate has a top surface area of $2m^2,$ and its edges and lower surface are well insulated. The plate is uniformly irradiated at its top surface at a rate of $1200$ W $.$ Consider steady state conditions for which $1000$ W of the incident radiation are absorbed$.$ The plate surface temperature is $350$ K and heat transfer by convection from the surface is $400$ W such that the net radiation is zero. Determine: $(10$points$)$

$($a$)$ The reflected incident radiation, in $\frac{W}{m^2}.$

$($b$)$ The emissive power, in $\frac{W}{m^2}.$

$($c$)$ Is the surface of the plate diffuse$-$gray? Prove your answer. $(+5$ BONUS points ${?}^1)$