Homework Statement
The universe is filled with EM radiation emanating from the Big Bang. This radiation was initially unimaginably hot but, as the universe has expanded, it has cooled to 3K. The distribution of the energy density of these photons in frequency (or wavelength) is given by the...
The question (1) wants you to prove equivalence in that all the equations in each system are linear combinations of the equations in the other system (I guess that B_11*x_1 + B_12*x_2 +...B_1n*x_n = (c_1*A_11+...+c_m*A_m1)x_1 +(c_1*A_12+...+c_m*A_m2)x_1 +...(c_n*A_1n+...+c_m*A_mn)x_1 = 0).
Homework Statement
Two problems.
(1) Prove that if two homogeneous systems of linear equations in two unknowns have the same solutions, then they are equivalent.
(2) Can you prove that the matrix
A = [1 1/2 ... 1/n
1/2 1/3 ...1/(n+1)
...
1/n 1/(n+1)...1/(2n-1)]...
Homework Statement
a straight horizontal rod slides along parallel conducting rails at an angle with the horizontal of 30 degrees (inclined plane). The rails are connected at the bottom by a horizontal rail so that the rod and rails form a closed rectangular loop. A uniform vertical field...
Homework Statement
Hint:Disregard any dissipative effects of the atmosphere of the planet.
A projectile is launched from the surface of a planet (mass M, radius R)
with a launch speed equal to 60 percent of the escape speed for that planet.
The projectile will rise to a maximum height and...
hmm...I guess it would depend on gravity (I originally looked at this problem and thought that the answer was just g, but my physics teacher told me I was wrong), because the total vertical acceleration apparently also (I think) depends on the angular acceleration.
The thin extension is attached to the rod in the same direction as the rod (i.e.) if I drew a picture it would sort of look like a corn dog:
------((((((((((((((
dist. from end of the thin extension to center of mass of rod = 6m
length of rod itself = 6m
so length of the thin extension = 3m
Homework Statement
A uniform rod of mass 1.6 kg is 6 m long. The rod is pivoted about a horizontal, frictionless pin at the end of a thin extension (of negligible mass) a distance of 6 m from the center of mass of the rod. Initially the rod makes an angle of 58 degrees with the horizontal...