Normalising Eigen vectors using Mathematica?

moment of inertia of a equilateral triangle about an axis passing through centre and perppendicular to the plane

. Because of the rotation of the earth, a plumb bob may not hang exactly along the direction ofthe earth’s gravitational pull (its weight) but deviates slightly from this direction. Calculate thedeviation (a) at 40 latitude, (b) at the poles, and (c) at the equator

The length of a massless rod is measured using vernier callipers having 10 vernier scale divisions and least count of 0.1 mm. Two masses 1.00 ± 0.01 kg and 4.00 ± 0.02 kg are attached to its ends. If reading of vernier scale is 5 divisions coinciding with 1.3 cm, what is the % error in locating centre of mass from lighter mass

A block is kept on x-y plane at a point (2m,3m). It is pushed with a force of magnitude 10 Ntowards point (5m,7m). The force can be represented as?

The phase of particle at t is 70°and another particle is at t is 790° what is wavelength if the distance between two particles is1 m