19 points. plz me. brainlist for first correct answer. i have an f in physical science. need to bring up the grade.

Space-time metric ds2= -dt2+at2dx2+bt2dy2+ct2dz2 (a)how does the area of a rectangle with vertices at ( x=0, y=0, z=0 ), (1,0,0 ), ( 0,1,0 ) and (1,1,0 ) changes with time? (b) if a photon moving in the x direction starts from the origin at t=1, when does it reach x=l? (ds=0 for the trajectory of a photon.) (c) the proper time for a particle is defined by cd=ds. what is the proper time for a particle to move along the trajectory ( x(t)=t, y(t)=0, z(t)=0 ) from t=0 to 1 ? what is the condition on the parameter a so that the velocity of the particle never exceeds the speed of light ?

If it takes a planet 2.8 x 10^8 s to orbit a star with a mass of 6.2 x 10^30 kg what is the average distance between the planet and the star

Athin electrical heater is inserted between a long circular rod and a concentric tube with inner and outer radii of 20 and 40 mm. the rod (a) has a thermal conductivity of ka = 0.15 w/(m*k), while the tube (b) has a thermal conductivity of kb = 0.8 w/(m*k) and its outer surface is subjected to convection with a fluid of temperature t= -15°c and heat transfer coefficient 60 w/(m2 *k). the thermal contact resistance between the cylinder surfaces and the heater is negligible. (a) determine the electrical power per unit length of the cylinders (w/m) that is required to maintain the outer surface of cylinder b at 15°c. (b) what is the temperature at the center of cylinder a?