Avector points into the third quadrant, and its x and y components are both negative. if its magnitude is equal to two times the magnitude of its x component, what is the angle between the vector and the positive x axis?

Explanation:

The vector lies in the 3rd quadrant, which means that both its x and y components are negative.

Let's analyze the magnitude now. We know that the magnitude of the vector (let's call it v) is 2 times the magnitude of the x-component:

we know that the magnitude of the x-component is given by

where here is measured as angle below the negative x-direction, since we are in the 3rd quadrant. Substituting into the previous equation,

But this is the angle between the vector and the negative x axis: therefore, the angle between the vector and the positive x axis is

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.