Vay

Let a matrix of a system of linear equations be W and a matrix that it is multiplied by as P. The order of coefficients corresponding to the variables for matrix W would be X, Y, and Z distributed across the row as X for the first column, Y for the second column, and Z for the third; however, this is ordered differently for the matrix of P, where the value of X, Y, and Z are distributed across in rows; where X is for the first row, Y is for the second, and Z is for the third. Is there a reason for the difference in order, or that there is really no reason to it and it is done for the sake of order? In short, why are multiplications of matrices ordered so that the dimensions of the multiplied matrices are that of m*n is multiplied with n*k. Or visually, the variables of matrix M, distributed horizontally, corresponds to the vertical distribution of the same variables of the matrix P, which matrix M is multiplied with. My textbook says this as a rule and doesn't explain why this rule is a rule: "Let A be an m X n matrix and let B be an n X k matrix. The product matrix AB is the m X k matrix whose entry in the ith row and jth column is the product of the ith row of A and the jth column of B." I have taken a guess at the reason, and the reason being that they are completely two different systems of linear equations (systems of linear equations A and B), so that the distributions of coefficient and variables are alternated, where the only similarity is that the horizontal coefficient of system A corresponds to the vertical variables of system B (relative to matrix A). The alteration is then only for the sake of organization?

Never mind, I am not thinking straight after doing my math homework for 6 hours straight, I will revisit this tomorrow. I get it when you explain it, I just have to repeat it in my head over and over again...

How about saying there are twice as many apples as there are oranges, so that for each orange there are 2 apples. Hence, 1 orange = 2 apples and 2 oranges= 4 apples, and so on? Is this the same? There are twice as many apples as there are oranges, so does this mean for each orange there are 2 apples, so that if apples=x and oranges=y, then y=2x; 2y=4x, and etc? I think the fault might lie in my misinterpretation, or maybe the statement is ambiguous.

My homework says there are "3/4 as many teenagers as preteens". Does this mean, when x=teenagers and z=preteens, that 3x/4=z or x=3z/4? This is a word problem for linear equations. I have done it both ways, and the book supports the fact that the answer is x=3z/4 when I looked at the answer at the back of my textbook, but I thought it was 3x/4=z according to the word problem and the not intention of the writer, so I wanted to verify with you guys. I think I am wrong, so how do you analyze this kind of problem involving "as"?

Thanks, I will not get married and have kids. The reason why I want to major in physics is not that I can wear it as a badge and show it off. I am genuinely interested in the wonders of our universe, but I will take the degree since it comes "free" for majoring in physics. I figured I only have one life, and before I die, I want to know as much about the world that has created me as possible. I know what I want to do, but the problem comes in what I want to do for money to support my life. I have had this question in my head since high school and it is a continuing question even until now in my life. If it matters, I am currently 18 years old. I went to college right after high school. I plan to transfer from art and advertising to CUNY Hunter College for a physics degree, and they accept on average 1/4 students who sign up for their school. I got my acceptance letter already. Hopefully those ahead of me in experience know what I might fall into. Thanks for the replies.

So I want to major in physics, but I don't care about the degree as much as the stuff I will learn. At least the degree will somewhat help me in finding some job. I am still young and I don't know what road to take, because apart from learning physics, I also want to write novels, become a painter, and hopefully have time to write or play music. I have played in a band before and I am pretty sufficient at drawing and painting. I have tried writing music, but have put it off since for school work and painting/drawing. I just don't know how much time I would have for these passions if I have a physics related job. On the other hand, I read that most physics graduates don't find a physics related job, so how does this work? Should I work as an artist and study physics on my spare time, or work as a physicist and do art on my spare time? Is it difficult to learn physics on your own?

I just figured out that we assume that a system of linear equations has a solution, then we proceed to solve it. But depending on the answer, then can we really claim whether it has a solution. Also the fact that a=b c=d then a+b=b+d as well, thanks.

So my textbook says multiply one of the linear equation until it can cancel out with another linear equation to get the solution for a variable, when the two equations are added. My question is, what is the proof or justification for adding equations that arrives to a solution? In other words, is this a mere coincidence that by adding the two equations, we can get the answer for a variable?

I stumbled upon the equation lim n -> infinity (1+(1/n))^n= e. My textbook says that the larger n is, the closer it gets to e. In calculating interest rates, n is replaced by amount of times compounded in one year. Anyone know why the irrational number e is so special? In that (1 + (1 divided by any large number)) an all to the power of the same very large number brings you close to e? This is utterly nonsensical to me. When this is applied to continuous compounding, where the compound amount A for a deposit of P dollars at an interest rate r per year compounded continuously for t years is given by A = Pe^rt. Does anyone know how did they derive the formula A = Pe^rt given the detail above? Also, do you think using the calculator too much can affect your thinking? In that you think less, so you are not as smart? Is it worth the trade off for a faster calculation? Also what do you think about teaching math where the you plug in numbers and teaching math where the teacher teaches how an equation is formulated?

If there is a proton and an electron, both exerting their respective force fields; the electron radiates its force inwards, while the proton radiates its force outwards. So does that mean when the proton and the electron are placed side by side, the proton is "sucked" towards the electron? How does this work? Which one is being "sucked" in? Are both moving towards each other?

Gravitational force between two bodies is equal to G*m1*m2/d^2. Does this formula work for finding the force of gravity without interaction with another body? Such that the gravity of a single isolated body is equal to G*mass/d^2? Or does it have to require an interaction? Also for F = M*a, this formula gives the instantaneous force at a particular location right? Is this the same for the force from G*m1*m2/d^2? Is gravity the only type of force that is affected by the inverse square law? I don't learn the math yet, because I am still in a basic physics course. But fortunately there is this forum. Thanks.

So the formula for Kinetic energy is KE=1/2*a*v^2 Where does the 1/2 come from? And the square is because the work required exponentially increases? KE = work, so that means work = 1/2*a*v^2? Therefore, 1/2*a*v^2= force x distance? Can anyone explain the help relationship?

I am confused about what is the shape of a black hole. I hear that it is a sphere and then it is a doughnut with a hollow middle, or are these two shapes the process of a black hole, with the black hole taking the shape of a sphere and then a doughnut? Can anyone clarify this?

If two people are experiencing the same gravitational pull in all respects, does location still un-synchronize their watches? I read in a book that put it a bit vaguely about how no where in the universe does time tick simultaneously.

But those two people are stationary, so how does time pass differently? Although the Earth accelerates the two subjects, the ground pushes back with the same force so they don't move anywhere. What probably happens is because they are at different positions on the Earth, when the Earth rotates, one subject is being accelerated more by the Earth's rotation so he experiences a difference in time, although it might be extremely minuscule. But this explanation does not work if two people are at different locations suspended in space in a free fall moving at the same constant speed.

I can understand why time will tick differently for two objects moving at different speeds, but why does time tick at different rates at different locations (or did I misinterpret something)? Edit: In other words, how do two people moving at the same speed have watches that tick un-synchronized just because they are at two different locations.

There are tons of them on amazon and I don't know which book is best. So if someone can recommend a good one, it will be greatly appreciated. I heard great things about this book: I am wondering if it has analytic geometry. http://www.amazon.com/Calculus-4th-Michael-Spivak/dp/0914098918/ref=sr_1_1?s=books&ie=UTF8&qid=1300050221&sr=1-1

I read that you need calculus to derive the equation for solving for the circumference of an ellipse. I am trying to use shapes as representation of force or orbital paths. I guess it would be much related to physics, but what I need most are the mathematical implications explained from a fundamental level. I don't have a lot of knowledge about categorization in mathematics, so it might not be calculus. I have been just visualizing most of the time and don't have the necessary mathematics to compliment with.

I need a book for the fundamentals of calculus that explains shapes, relativity, and movement etc (e.g. elliptic movements). I don't know where to look because I can find mostly text books that cost a lot, which I don't want to buy. I was hoping to find some old theory books that are re-translated if they existed.

How do objects get shorter? Do they get shorter beginning from the point which is towards the direction of the object's displacement to the opposite end of that point on the same object? If a car was driving forward extremely fast, then the car will get shorter at the front and back? So what about the top and bottom? Which raises the question, is it possible for something to move in all directions at once without splitting itself up (Does this deal with the uncertainty principle about inability to locate exact position and movements of electrons?)? Also, is the decrease of an object's length a proportional decrease based on the object's stable length or is it a constant decrease based on how fast something is moving?

So that means the guy inside the rocket will see the outside world speeding up?

If you are looking at Earth from outer space, you could see Earth spin right? While on Earth we can't feel the spin or the Earth move because time has slowed down for those on Earth. Is the acceleration significant enough for this difference? Also, if time slows down when you move fast, then how are you moving fast if time has slowed down? I remember reading in a book that when driving in a car, time inside the car would be slowed down in respect to the outside, so does it apply to the car itself as well, because if it does, then how does the car move faster and not slower?

i want to learn about mechanics such as the movements of a bionic arm, but since it is a decently new topic in science, i wouldn't think i might find much. So if you can recommend a good reliable book that just introduces mechanics to its reader would be fine..

I don't know anything about bionics and I want a good book that introduces bionics so i can learn the mechanics behind Bionics and how a human mind can control machine. So far i haven't gotten any luck "googling" or "amazoning"....you just get fiction books and some $100 text book. I would have gone with the $100 text book but i don't know if it is good as an introduction to bionics or is it reliable. so as the title says, can any1 recommend a book that introduces bionics? maybe there are also physic books or engineering books that introduces bionics?

can someone explain how it expands or contracts on a complex plane? The first time i tried to see how it works, i used real numbers, but is there a difference or am i doing something wrong because the triangles as a result are not similar.