A rod of length Lo moves iwth a speed v along the horizontal direction. The rod makes an angle of (θ)0 with respect to the x' axis. Required:
a. Show that the length of the rod as measured by a stationary observer is L=L0[1-v^2/c^2 cos^2(θ)0].
b. Show that the angle the rod makes iwth the x-axis is given by the expression tan(theta)=tan(θ)0/(1-v^2/c^2)^.5

From the question we are told that

  The length of the rod is  

    The  speed is  v  

     The angle made by the rod is  

Generally the x-component of the rod's length is  

Generally the length of the rod along the x-axis  as seen by the observer, is mathematically defined by the theory of  relativity as

=>    

Generally the y-component of the rods length  is mathematically represented as

Generally the length of the rod along the y-axis  as seen by the observer, is   also equivalent to the actual  length of the rod along the y-axis i.e

    Generally the resultant length of the rod as seen by the observer is mathematically represented as

=>  

=>  

=>  

=>

=>

=>

Hence the length of the rod as measured by a stationary observer is

   Generally the angle made is mathematically represented

=>  

=>

Explanation:

answer: the metamorphic rocks are formed when they are exposed to high pressure and high temperatures. this happens when one of the earth's plates comes in contact with the other plate by traveling in opposite directions, straight into each other or slipping under one another. the friction that is caused by this activity results in   melting of rocks and when it cools they are known as metamorphic rocks. this process needs a controlled amount of pressure and temperature otherwise it may turn into magma.