What is the five things to do in P. E

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 ?

Considering only the earth's rotation, determine how much later the asteroid would have had to arrive to put the explosion above helsinki at longitude 25˚ e? this would have obliterated the city.

Consider a hydrogen atom in the ground state. what is the energy of its electron? =e= jj now consider an excited‑state hydrogen atom. what is the energy of the electron in the =5n=5 level? =e5= j