The scalar product between two 3-vectors can be written ab= ab cos ab, where a and b are the magnitudes of the vectors and eab is the angle between them. show that an analogous formula holds for two timelike 4-vectors a, b: a b= -ab cosh (abs (2) where a = (-a. a)1/, b = (-6. b)/2 and vab = tanh oab, for vab being the lorentz boost between the frame in which an observer whose worldline points along a is at rest and the frame for which an observer whose worldline points along b is at rest.

Orque can be calculated by multiplying the force (n) applied at 90? to the lever arm at a distance (m) from the pivot point (point of rotation), the compound si unit for the torque is n? m. if the force (at 90? to the lever arm) applied is 15 n and it is applied at 2.0 m from the pivot point (point of rotation), what is the torque on the lever?

Suppose that two tanks, 1 and 2, each with a large opening at the top, contain different liquids. a small hole is made in the side of each tank at the same depth 1.57 m below the liquid surface, but the hole in tank 2 has 2.49 times the cross-sectional area of the hole in tank 1. (a) what is the ratio ρ1/ρ2 of the densities of the liquids if the mass flow rate is the same for the two holes? (b) what is the ratio rv1/rv2 of the volume flow rates from the two tanks? (c) at one instant, the liquid in tank 1 is 14.9 cm above the hole. if the tanks are to have equal volume flow rates, what height above the hole must the liquid in tank 2 be just then?

What tightening torque should be used for a hexagonal head screw (not split-bolt) on a 250 kcmil conductor?