Alan

You are correct Melody.

Applying the cross multiplication solves for.. meaning what's at the root of it, what does it do exactly?

Imagine you are in a spinning extra-vehicular harness in space (like George Clooney in the film Gravity).  You have to fire your pneumatic boosters to counteract the spin.  The reaction force from the gas jet is a vector, as is the radius arm from your centre of gravity to the gas jet.  The cross-product of these two vectors tells you the magnitude and direction of the torque being supplied to counter your spin (or to increase your spin, or set you tumbling in a different direction, if you get it wrong)!   

There are many more down-to-earth applications of the vector cross-product, often involving rotating objects.

 … if you do not have all the variables for the matrix will it generally come down to a quadratic or similtaneous equation which is solved by a matrix?

I don’t understand what you are asking here.  The matrix determinant form of the cross-product is just a way of remembering which components are multiplied by which in each direction! 

Find out how many standard deviations 6 is from 9.5 and look up the probability, or, better in this case, just look at a graph of the probability density function like below (assuming the distribution is normal).

If you look at the graph, does it seem likely that fewer than 6 people would have heard of Yummy?  Strictly, the graph shouldn't go above 12, so using a normal distribution is an approximation.

Radiated energy is proportional to absolute temperature to the fourth power.

$$16^\frac{2}{3} = (2^4)^\frac{2}{3}=2^\frac{8}{3}=(2^6)^\frac{1}{3}\times(2^2)^\frac{1}{3} = 2^2\times(2^2)^\frac{1}{3}=4\times4^\frac{1}{3}$$

or

$${{\mathtt{16}}}^{\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)} = {\mathtt{6.349\: \!604\: \!207\: \!872\: \!797\: \!4}}$$

An interesting algorithm! It only tells you the number of final zeros though.  You could check this by counting all the zeros in 486! or, alternatively, use the algorithm on, say 7! (=5040).

Exactly 2.54 cm = 1 inch

Momentum is mass*velocity.

Cheetah: 74*31 = 2294 kg-m/s

Elephant 7000*18000/3600 = 35000 kg-m/s