Ameasure of the disorder of a system is called

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 ?

What is the electric force acting between two charges of -0.0045 c and -0.0025 c that are 0.0060 m apart? use fe=kq1q2/r^2 and k = 9.00 x 10^9 n*m^2/c^2 a. 1.7 x 10^7 n b. -1.7 x 10^7 n c. -2.8 x 10^9 n d. 2.8 x 10^9 n

What is the magnitude of the acceleration vector which causes a particle to move from velocity −5i−2j m/s to −6i+ 7j m/s in 8 seconds. answer in m/s.