In the Video for Shark in the Water by V. V. Brown?

That's a new character in the world of Degrassi, Eli, and I also have my predictions about him in the season: Most likely Eli and Clare date, hence the 'Lovers' card, but the death card is a harder guess. Maybe they do not last?Maybe someone dies? Or maybe, and I am just throwing a bone here, it indicates the would eath' of the school, hence the lock down. What confuses me is why Clare seems worried while Eli seems unfazed. It's possible he kills someone or maybe, if I am right about the lock down, he has not gone to Degrassi long enough to care.

1. Prove that the map $phi: V

ightarrow V^*$ is surjective

From your previous question you already know that $phi$ is injective. Because $V$ is finite-dimensional and you mention the dual basis I assume you know that $dim V = dim V^*$.We have the following well-known result:Therefore we can follows from the injectivity of $phi$ that it is also surjective.

2. Prove that there is a natural isomorphism between $V$ and $(V^*)^*$

For every vector $v in V$, you have to produce some $i(v) in V^**$. And this one must be a linear map$$ i(v) : V^* longrightarrow mathbbK . $$So, you have to produce an element of $mathbbK$, for every $omega in V^*$. That is$$ omega mapsto i(v)(omega ) . $$Now, having as all data a linear form $omega in V^*$ and a vector $vin V$, how would you obtain, in the more natural way, an element of $mathbbK$?

3. Words that start with V?

vector, verify, veracity, validate, voracious, villae, vermiform, vulva, mons veneris, acne vulgaris, vinca alkaloids, vacuum, vacant, vanguard, van, vaccuous, vortex, varrucae, varicella, variola, virus, vindictive, vindication, venifer, vein, venous, venule, venerial, vocal, vehicular, vent, virile, virilization, vibrio cholerae, vamp, vampire, Van der Waals, Von Willibrand. That is all I can think of right now

4. 08 mustang v-6 to v-8 swap?

u will need the entire drive train from a donor car.......engine trans computer drive shaft traction controlled rear-end radiator.......basically if would b easier to buy a cobra and remove the badgeing and put v6 badgeing and body parts on it.

5. Mercedes Benz v. BMW v. Porsche?

The BMW and MB are V8 engines, so the Porsche with its opposed 6 cylinder is probably the most efficient. But when you are spending that much money to lease a car, why is gas mileage a concern? They all meet federal safety standards, but since the Porsche is rear-engined, the other two cars with engines in front would be better in a front end crash. Convertibles are the worst cars for rollovers because the only protection is the windshield pillar frame. I would guess the MB would be slightly better than the BMW, but BMW's are amazingly well-constructed and protect the passengers very well. You can probably get more data from the IIHS (Insurance Institute for Highway Safety.) Most luxurious would be the MB, with BMW in the #2 slot and Porsche, well, that's a racing car disguised as a daily driver. If it were my choice, I would take the BMW 650i - I have a 3 series and I would not hesitate to buy another BWM if I was in the market for a new car. The car is well-designed, manufactured to high quality standards and the performance and road handling is excellent. But your father really can not go wrong with any of the three. Why not rent one of each of the cars for an extended test drive over a weekend? Not sure where you live, but many cities have specialty car rental companies for luxury and performance cars. Or just rent a demo car from each of the dealers for 3 days. Good luck. Too bad we all do not have your dad's "problem."

6. Is it possible to store flyback voltage in capacitors?

In principle, yes. In practice, already doing it.Consider the workings of a flyback diode. When the current to a motor is turned off, the energy in its windings (i x i x L / 2) needs someplace to go, and without the diode will produce a high voltage spike (V = L di/dt). The energy which needs to be transferred is shunted back into the motor power supply by the diode, and is soaked up by the output capacitance of the supply.So the idea is not totally without merit - it's just that it's already happening.

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