The derivation of Einstein's most famous equation E = mc² is purely theoretical, which arises as a direct consequence of his Special Theory of Relativity that involves some algebraic manipulations using the Pythagorean theorem (SPM level). To understand how he derived the equation, you must understand a portion of his Special Relativity; Time Dilation (see the embedded Spaceship figure). The following derivation is highly simplified for the mathematically untrained. To further enhance your understanding, you should watch the YouTube video by minutephysics.

Hi can anyone here explain what the point v=0 is not situated at the left side of charge 5q or right side of charge -2q?? V=electric potential

49.49? 

     
     
     
     
     


P.S I think my notations are a little bit misleading, by sum from 3 to 99, I mean the sum of odd numbers only, 3, 5, 7, 9....99

So, my hypothesis on passing the Pure Math exam with flying colors has a good degree of trueness.

5?

The question can be solved algebraically using knowledge learned from SPM Progressions, Indices and Logarithms.



which can be rearranged to give

.

By letting

,

we need find integer n which satisfies



Using a graphing software, one can evaluate

1/5050, 5049?

I did it using similar method as the last question.

Hi Critical_Fallacy and crazywing26, I would like to ask you something concerning matrices.

Suppose that we have a 3 x 3 matrix A, and that we have to find it's determinant.


From the above matrix A, it's determinant can be evaluated by adding the products of any elements with any one row(with it's column) with their respective cofactors. It should be like this:


But, I too found out that there is another alternative way to solve the determinant of a 3 x 3 matrix, that is by using Sarrus' Rule. It's the sum of the multiplication of entries in every arrow to the right(blue colour) minus the sum of multiplication of entries in every arrow to the left(red colour).


Now my question is, as far as I know from my book, Sarrus' Rule is not mentioned in it. If by any chances were I to stumble across a question concerning the determinant of a 3 x 3 matrix, can I use Sarrus' Rule? My reason is that it's way more flexible and less tedious compared to the other method in which we need to first find the minor and cofactor first. But, knowing that sometimes the marking scheme for STPM is extremely stringent and rigid, I feel that it's not a safe bet. Any Form 6-ers have experience this before?

Another thing I would like to know is why the signs of the 3 x 3 matrix (cofactors) should be like this ? :

I'm quite flabbergasted regarding the above bold statement. I never knew that the way the markers mark is this stringent and complicated. Anyway, thanks for that heads-up. Now I know a little bit on what I should and should not do in the near future.

To find determinant of 4x4 matrices would it be very tedious then?

Thanks for the insight.

Anyway this is too advanced, 1st year uni calculus, cannot use calculator for exam.

To find the determinant for 4X4, the formula is cofactor-cofactor+cofactor-cofactor? Do you get what i meant?

Critical_Fallacy and v1n0d

Look at what I found !

http://eprints.usm.my/view/subjects/

Let A be an (n x n) matrix satisfying 2I - A = A^5. Find an expression for the inverse of A.

2(AA*-1) = A*5+A
A*-1 = (A*5+A/2A)
A*-1= 1/2A*4 + 1/2

This is my answer, but the answer sheet says
A*-1 = 1/2A*4 +1/2I ( why is there an I?) anyone can explain it to me ? @Critical_Fallacy

They say I'm weird but delicious things like this make me go "    " . I actually prefer this ( although I understand 0.1% of it ) to parties and countdowns .

I still haven't found a friend who has the same wavelength as me . 

Hopefully at uni , I'll finally be able to talk to someone whose eyes glimmer when reading about stuff like the curving of space-time , even in layman's terms . Nobody is interested in what I'm interested in . Everyone's so career oriented that I want to get out of this shell , this small fishing village to somewhere which hopefully would provide me with academic stimulation which I'd really appreciate .

I've been living for 18 years ( almost ) as a lonely kid , thank Goodness there's this thing called the internet . 

sorry i seek money and waifu only 

Accounting & Finance, at LSE 

Parents are both accountants. Pathway laid out edi. 

As you probably already know, we don't actually divide matrices. Try this: