And I'll just switch colors arbitrarily.

I'II change the sign. Please Ieave. go!

So let me just switch sides as well.

I'll switch colors arbitrarily.

I'm not switching the ratio on you.

I should switch colors.

Min Hee! Switch the positions of the two actors.

Because we've essentially just swapped the x and the y.

And if we want to write it back in terms of the sulfate terms, we can just un substitute the x, and we're

So it switches the sign here, so it becomes plus b d.

And in this case, you just switch these two terms.

I just un substituted the x plus three molecules of water.

We've essentially just swapped the x's and the y's.

We've essentially swapped the x and y.

So either way you do it, it'll work.

It struck me how often Dorian changed his servants.

When you substitute j here, you get g of x.

But when we swap the x's and y's, this is going to be our domain.

And keep in mind, I actually swapped the left and the right hand sides.

So if you substitute that there, what does our whole expression equal?

Alice would need to apply a shift of 3 to each letter in her original message,

And once again, it makes complete sense because we've swapped the x's and the y's.

And by presenting a really strong economic case, they convinced the L.A. government that replacing that asphalt with trees and other greenery, that the schools themselves would save the system more on energy than they spend on horticultural infrastructure.

We have distance is equal to the initial velocity plus the final velocity, so let's substitute this expression right here.

And then we had the 2 replaced where the 7 is.

left with one molecule of iron oxide plus three molecules of sulfuric acid, H2SO4 I just un substituted the x with SO4

And notice, we're just switching the direction in the imaginary along the imaginary axis, when we take the conjugate of something.

Then Bob simply subtracts the shift of 3 from each letter, in order to read the original message.

Now, you should hopefully be reasonably convinced that we can do this, that you can change your basis and find a transformation matrix.

Caesar shifted each letter in his military commands in order to make them appear meaningless should the enemy intercept it.

For example, the Caesar cipher shifted every letter by the same shift, which was some number between 1 and 26.

Moreover, a change in China s exchange rate would do little to alter the multilateral trade deficit in the US.

So if we just swap these around and change the order in which we're multiplying, we can write this as a times a times a times b times b times b.

For the reciprocal of 7 4, you swap the numerator and denominator, or the top number and the bottom number, and you get 4 7.

Whenever they needed to denote a chapter break or a division of text, scribes would switch from standard black to the red pigment, minium.

Well look, if you take this, if you assume this part right here, then we can replace each of these i's with the square root of negative 1 And they'd be right.

But the general idea, we just swapped the x's and y's between this function and this function right here, if you assume a domain of positive x's and positive y's.

In the rightmost example below, an element of order 7 of the (2,3,7) triangle group acts on the tiling by permuting the highlighted warped triangles (and the other ones, too).

Another fantastic case of creating intangible value to replace actual or material value, which remember, is what, after all, the environmental movement needs to be about

How would the exchange rate be set for the new currency? The obvious choice would be to start by exchanging one new franc for one euro and then leave it to the global currency markets to re price the new currency.

And by presenting a really strong economic case, they convinced the L.A. government that replacing that asphalt with trees and other greenery, that the schools themselves would save the system more on energy than they spend on horticultural infrastructure.

And let's replace the second row with the second row minus the first row.

Because although many of the speakers and many of the people who are in the audience, although you guys can not only go to the moon, you know, you're going to totally transform everything.

Another fantastic case of creating intangible value to replace actual or material value, which remember, is what, after all, the environmental movement needs to be about This again is from Prussia, from, I think, about 1812, 1813.