The boy beetle rubs his antenna against the girl beetle.

Looked like a ladybug, right?

I mean, a stag beetle it's got two points for jaws, it's got antennae.

This beetle, unlike this chip bag here, this beetle uses one material, chitin.

And what does the girl beetle do?

Here are the beetle brows shall blush for me.

Call that beetle! Call anybody!

Hear that beetle talk... you'd think somethin' was gonna happen to us.

Now, Atlantic spotted dolphins are a really nice species to work with for a couple of reasons.

Turning rocks over revealed this crab spider grappling with a beetle.

It's your ship.

We can easily tally the costs of individual conservation efforts like saving the northern spotted owl.

I traveled to over 40 countries to see jaguars and bears and elephants and tigers and rhinos.

In the first video on evolution, I gave the example of the peppered moth during the Industrial Revolution in

The longhorn beetles (Cerambycidae also known as long horned beetles or longicorns) are a cosmopolitan family of beetles, typically characterized by extremely long antennae, which are often as long as or longer than the beetle's body.

Right by twos!

I mean, a stag beetle it's got two points for jaws, it's got antennae. Can you be that specific in the detail?

Two by two. Right and left.

So it's 1, 0, 2 0, 1, 2 2, 3, 0, just like that.

0 minus 2 is minus 2.

1, 2, minus 1, 0 times minus 2 minus, minus 2. And so what would this be equal to?

So the transformation of x2 is equal to our transformation matrix 1, 2, minus 1, 0 times 2, minus 2. And so this will be equal to 1 times 2 is 2. Plus minus 1 times minus 2.

Then upper triangular, everything below the diagonal is a 0, and everything above the diagonal probably isn't a 0, but you never know.

0 minus 2 is minus 2.

The upper triangular everything below the diagonal.

And over the last decade, I traveled to over 40 countries to see jaguars and bears and elephants and tigers and rhinos.

So this matrix right here.

I'm ignoring the zero because it's in the same column as the 1, 2, 0 0, 2, 3, and then 2, 0, 0.

1 minus 2 minus so it's 1 minus 2 plus minus 1 times minus 2. That's going to be plus 2.

Don't give them four, give them two plus two.

Minus 2 times minus 2 is 4.

Two!

Two.

Two.

Let's take our transformation of x2.

Everybody knows that two and two make four.

This just comes from the definition of a 2 by 2 determinant.

2 minus 2 times 1 is 0.

One, two, three, four, one, two, three, four.

So it's minus 2 plus a plus 2, so it's equal to 0.

We defined the determinant of a 2 by 2 matrix not in terms of a determinant.

0 minus 2 times 1, that's minus 2.

Two plus two equals four, and one is just one.

2 minus 2, times 1, is 0.

5 minus 2, times 2, is 1.