Show that the expressions (ds)2 (c dt)2- (dx)2 - (dy) - (dz)2 is invariant (i. e, a scalar quantity) under lorentz transformations. this is the "four-dimensional distance" between events and is also known as the metric. show that if (ds)2 < 0 the two events cannot be causally connected, i. e., there cannot not be any information transmitted from one to the other even at light speed

Very large accelerations can injure the body, especially if they last for a considerable length of time. one model used to gauge the likelihood of injury is the severity index ( ), defined as =/ . in the expression, is the duration of the accleration, but is not equal to the acceleration. rather, is a dimensionless constant that = the number of multiples of that the acceleration is equal to.in one set of studies of rear-end collisions, a person's velocity increases by 13.7 km/h with an acceleration of 36.0 m/s2 . let the + direction point in the direction the car is traveling. what is the severity index for the collision?

An electric clothes dryer has a resistance of 8 ohms. it draws 30 a of current. what is the voltage, in volts, of the wall outlet that it is plugged into?

Find the equation for the plane through upper p 0 left parenthesis negative 4 comma negative 8 comma negative 5 right parenthesis perpendicular to the following line. xequalsnegative 4 minus t, yequalsnegative 8 plus 2 t, zequals3 t, minusinfinityless thantless thaninfinity