Two blocks in a system (b1 & b2) collide inelastically where
b1 has a velocity (v) and a small mass (m) and b2 is stationary
with a large mass (M). b2 can absorb some of the collision similar
to a spring that does not recoil with a stiffness of (k). When the
blocks collide they will stick together. The plane that the blocks
are moving on is horizontal and frictionless.
1)Find the change in internal energy (delta U)
2)If all...
The period T of a simple pendulum is given by T=2π√L/g where L
is the length of the pendulum and g is the acceleration due to
gravity. Assume that g = 9.80 m/s^2 exactly, and that L, in meters,
is lognormal with parameters μL = 0.6 and σ^2L=0.05. NOTE: This is
a multi-part question. Once an answer is submitted, you will be
unable to return to this part.
Find the mean of T.
Find the median of T.
Find the...
Show that in any finite gathering of people, there are at
least two people who know the same number of people at the
gathering (assume that “knowing” is a mutual relationship). Hint
available.
Let V be a finite-dimensional vector space over C and T in L(V).
Prove that the set of zeros of the minimal polynomial of T is
exactly the same as the set of the eigenvalues of T.
Suppose A=(7B^n)/(CD), where A has dimensions [T]/[L]^3, B has
dimensions [T], C has dimensions [T][M]^2, and D has dimensions
[L]^3/[M]^2. Using dimensional analysis, find the value of the
exponent n.
Consider two boxes B1 and B2. B1 has 10 red and 3 green balls
where B2 has 6 red and 4 green balls. You are selecting one ball at
random from B1 (Without replacement) and adding that to B2.Finally
selecting one ball from B2. Find the following probabilities
a) What is the probability of selecting a red ball from B1? (3
points)
b) What is the probability of selecting a red ball from B2? (7
points)
(a) Show that a group that has only a finite number of subgroups
must be a finite group.
(b) Let G be a group that has exactly one nontrivial, proper
subgroup. Show that G must be isomorphic to Zp2 for some prime
number p. (Hint: use part (a) to conclude that G is finite. Let
H
be the one nontrivial, proper subgroup of G. Start by showing
that G and hence H must be cyclic.)