Find the transformation matrix that rotates a rectangular coordinate system through an angle of 60 about axes equal angels with original three coordinate axes

Explanation:

To find the matrix, let's decompose the vectors, the rotated angle is (-60C) for the prime system

          x ’= x cos (-60)

          y ’= y sin (-60)

we use

          cos 60 = cos (-60)

          sin 60 = - sin (-60)

we substitute

          x ’= x cos 60

          y ’= - y sin 60

the transformation system is

         x '

the transformation matrix is

i would like to make dinner for my mom, dad, and sister

speed of light in vacuum is 300,000 km/s

speed of light in other mediums is given by the expression v = c/n, where c is the speed of light in vacuum and n is the refractive index of medium.

for the first medium v = 200,000 km/s

  so, refractive index of medium = 300000/200000 = 1.5

    1.5 refractive index is usually for glass. so first medium is glass.

for the second medium v = 250,00 km/s

so, refractive index of medium = 300000/250000 = 1.2

    1.2 refractive index is usually for water. so second medium is water.

for the third medium v = 0 km/s

so, refractive index of medium = 300000/0 = ∞

    ∞ refractive index is usually for opaque mediums. so third medium is opaque medium.