A is an n\times n matrix. check the true statements below:

a. an eigenspace of a is just a null space of a certain matrix.

b. if v_{1} and v_{2} are linearly independent eigenvectors, then they correspond to distinct eigenvalues.

c. if ax = \lambda x for some nonzero vector x, then \lambda is an eigenvalue of

a.

d. if ax = \lambda x for some vector x, then x is an eigenvector of

a.

e. the eigenvalues of a matrix are on its main diagonal.

1400 kg car has a speed of 27 m/s. if it takes 7 s to stop the car, what is the impulse and the average force acting on the car?

In the derivation of rrkm theory, a factor of 1/2 is introduced when equalizing the rates of formation and decomposition of activated complex as keal-hr) = ko this is clearly against the assumption of transition state theory that states all the activated complex in the transition state iss going to the product. find the reason why this factor is introduced here.

The intensity of a polarized electromagnetic wave is 12 w/m^2. part a) what will be the intensity after passing through a polarizing filter whose axis makes the angle θ=0∘ with the plane of polarization? part b) what will be the intensity after passing through a polarizing filter whose axis makes the angle θ=30∘ with the plane of polarization? part c) what will be the intensity after passing through a polarizing filter whose axis makes the angle θ=45∘ with the plane of polarization? part d) what will be the intensity after passing through a polarizing filter whose axis makes the angle θ=60∘ with the plane of polarization? part e) what will be the intensity after passing through a polarizing filter whose axis makes the angle θ=90∘ with the plane of polarization?