A 1,383 kg purple car is driving southbound on a road and collides with a 1,827 kg orange car, that was traveling 31.87 m/s eastbound. The two cars collide and stick, sliding 14.54 meters before coming to rest. What was the initial velocity of the two-car system just after the collision? Take the coefficient of friction to be 0.463, and the acceleration due to gravity to be 9.8 m/s2. Answer to two decimal places.

Let v1, v2, w be three linearly independent vectors in r 3 . that is, they do not all lie on the same plane. for each of the following (infinite) set of vectors, carefully sketch it in r 3 , and determine whether or not it is a vector space (i.e., a subspace of r 3 ). explain your reasoning

Suppose that an electromagnetic wave which is linearly polarized along the x−axis is propagating in vacuum along the z−axis. the wave is incident on a conductor which is placed at z > 0 region of the space. the conductor has conductivity σ, magnetic permeability µ and electric permittivity ε. (a) find the characteristic time for the free charge density which dissipates at the conductor. (b) write the maxwell equations and derive the wave equation for a plane wave propagating in a conductor. (c) find the attenuation distance at which the incident amplitude reduces to e ^−1 of its initial value. (d) find the electric and magnetic fields inside the conductor. 8 (e) find the power loss per area of the incident electromagnetic wave at the surface of conductor.

Much of the information taught in earth-space science would not be available if it weren’t for our remote sensing abilities. explain two ways our remote sensing strategies contribute to our knowledge of these topics.