a)Does the vibrational frequency of an O-H bond depend on whether it is horizontal or vertical at the surface of the Earth? Suppose that a harmonic oscillator of mass m is held vertically, so that it experiences a perturbation V(x)=mgx, where g is the acceleration of free fall. Calculate the first order correction to the energy of the ground state.

b) Repeat the previous exercise to find the change in excitation energy from v=1 to v=2 in the presence of the perturbation.

The nose of an ultralight plane is pointed south, and its airspeed indicator shows 39m/s . The plane is in a 12m/s wind blowing toward the southwest relative to the earth.

Question A:

Letting x be east and y be north, find the components of v? P/E (the velocity of the plane relative to the earth).

Question B:

Find the magnitude of v? P/E.

Question C:

Find the direction of v? P/E.

Any help is appreciated!

Does the weighting function in the prospect theory magnify the importance of very low and very high probabilities? Why and how?

Prospect Theory offers an alternative framework to making decisions by expected utility maximization. It allows for these realistic behaviors exhibited by investors:
I) Having better prospects if seen next to an irrelevant, slightly flawed, alternative

II) Measuring success with respect to an (arbitrary) reference point

III) Loss aversion

IV) Tolerance for ambiguity when faced with the prospect of extraordinary gains

V) Stronger reactions to losses than to gains of the same magnitude

a. II, III and V

b. I and IV

c. I and II

d. III, IV and V

e. II and V

1. Name the two different kinds of friction and briefly describe them.         
2. The data below for the instantaneous velocity v versus the time t were obtained in a level 300 student experiment. Perform a linear least square fit with v as the vertical axis and t as the horizontal axis.

Table 1: v versus t

Determine from the graph;

2. 1. Acceleration a
   2. Initial velocity v_o - (Intercept)          
3. Mention the equipment used to measure the following quantities in the laboratory and state their corresponding SI unit of measurements;
   1. Voltage
   2. Current

Magnetic flux density           

Use the link Standard Reduction Potentials to answer the following questions.
For each pair of redox couples, write a balanced redox equation, determine the cell potential and the number of electrons transferred. Use the lowest possible coefficients. Include states-of-matter in your answer.

In this discussion, you'll describe a patient with a mood disorder and the appropriate nursing interventions. Please answer the following questions in your initial posting:

Describe a client from your clinical setting or previous experience who experienced depression or mania. Include a brief history and 3-5 most pertinent medications.

v Identify one problem that was not resolved with the treatment regimen. What are the reasons it may not have been successful? Include nursing as well as other team members.

v Identify one effective nursing intervention and why you feel it worked.

v Overall, do you feel this client was kept safe? Why or why not?

v Please provide supporting evidence for your answers.

Your driving time to work T (continuous random variable) is between 22 and 64 minutes if the day is sunny, and between 41 and 86 minutes if the day is rainy, with a uniform probability density function in the given range in each case. Assume that a day is sunny with probability p subscript s = 0.41 and rainy with probability p subscript r equals 1 minus p subscript s. Your distance to work is X = 60 kilometers. Let V be your average speed for the drive to work, measured in kilometers per minute: V equals X over T Compute the value of the probability density function (PDF) of the average speed V at V = 0.62

V owns 80% and his friend, W, owns 20% of a partnership. After transferring 30% of the capital and profits interest to his son, R, V's interest drops down to 50% of the partnership. Partnership profits of $200,000 for the year were allocated as follows: $100,000 to V, $60,000 to R, and $40,000 to W. Two years later, an IRS audit revealed the following: •Only V performs services for the partnership and they were worth $52,000. •Ending capital accounts were $200,000 for V, $40,000 for R, and $60,000 for W. Capital is a material income-producing factor. Which of the following is the maximum increase to V's includible income by the IRS? A. $19,500 B. $26,000 C. $42,000 D. $50,667

3. True or false? All vectors below are in Rⁿ for some n. If your answer is “True”, explain why. If your answer is “False”, give a counterexample. Please specify for all if the given statement is true or false, thank you!

(1) If two vectors are linearly independent, then they are orthogonal.

(2) If x is orthogonal to both u and v, then x must be orthogonal to u − v.

(3) If W is a subspace of Rⁿ, then W and W^⊥(W transpose) have no vectors in common.

(4) If z is orthogonal to v₁ and v₂ and if W =span(v₁,v₂), the z must be in W^⊥​​​​​​​(W transpose) .

(5) ∥cv∥ = c∥v∥ for all scalars c and vectors v in Rⁿ .