In an ionic crystal, the coupling of the transverse optical photon

In an ionic crystal , the coupling of the transverse optical phonon with the electromagneticwave leads to polariton with the dispersion relation given as :"K ? C 2 / 0 2 = E ( W ) = $ ( 00 ) + [ { ( 0 ) – $ (00) ] WOT ? / ( WOT ? _ W 2 ), where IT is the frequency of the transverse*phonon mode , & is the wave vector of the polariton . ( a ) ( 10pts ) Find the solutions for w near k = 0and k being very large ; ( b ) ( 10 pts ) Discuss if the polariton wave can propagate in the frequencyrange (T < W < WL , where we ( the frequency of the longitudinal mode ) is related to cut through the[ST relation ( eq . 62 , ch . 14 ) .E-E ( 0 )E ( 00( 62)

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In an interview on CNBC, a major shareholder of JW’s common stock (a known activist investor) stated that JW’s management is holding too much cash and that some of this liquidity s hould be reinvested in the firm. Consequently, the CFO will lower the Cash Ratio by using cash and equivalents to purchase operating assets (i.e., the firm’s total asset base will not change). What level of cash and equivalents is required to generate the following values for the Cash Ratio

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In an interest-rate swap transaction, Large corporation Limited can borrow in the bond market at a current fixed rate of 9 percent and can also obtain a floating-rate loan in the short-term market at the prime bank rate. However, this firm wishes to borrow short-term because it has a large block of assets that roll over into cash each month. The other party to the swap is Small corporation Limited, with a lower credit rating that can borrow in the bond market at an interest rate of 11.5 percent and in the short-term market at prime plus 1.50 percent. Small corporation Limited has long-term predictable cash inflows, however. Large corporation Limited wishes to pay for its part in the swap an interest rate of prime less 50 basis points. Small corporation Limited is willing to pay the underwriting cost associated with the Large corporation Limited ‘s security issue, which is estimated to be 25 basis points. The swap transaction is valued at US$100 million

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In an inkjet printer, tiny drops of ink of inertia m are given a charge q and then fired toward the paper at speed v. They first pass between two charged plates of length ℓ that create a uniform electric field of magnitude E between them (Figure 1) . The field direction is perpendicular to the plates and to the initial path of the drops. The electric field deflects each drop from its initial horizontal path and is used to control what is printed on the paper.

Part A

Derive an expression for how far in the vertical direction a drop is deflected as it passes between the plates. Use the notation l for the length of the plates ℓ.

Part B

For a drop inertia of 1.0×10−10 kg , an electric field strength of 1.4×106 N/C , a plate length of 17 mm , and a drop speed of 29 m/s , calculate the drop charge necessary to result in a deflection of 1.3 mm.

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In an inertial frame, an object cannot remain at rest unless which of the following holds?

a. The net force acting on it is zero.

b. There are no forces at all acting on it.

c. The net force acting on it is constant.

d. There is only one force acting on it.

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