System Definition and 1000 Threads

So, my linear algebra book, if you can call it that, says the following: $Ax=b$ is a system of linear equations with $m$ equations and $n$ variables. ${v}_{1}, {v}_{2}, ..., {v}_{n}$ are the vectors in the columns of $A$. The following are equivalent: (1) The system $Ax=b$ is possible for...

Homework Statement With respect to a given Cartesian coordinate system S , a vector A has components Ax= 5 , Ay= −3 , Az = 0 . Consider a second coordinate system S′ such that the (x′, y′) x y z coordinate axes in S′ are rotated by an angle θ = 60 degrees with respect to the (x, y) coordinate...

Homework Statement Question attached: Hi, To me this looks like a classical, continuous system, as a pose to a quantum, discrete system, so I am confused as to how to work the system in the grand canonical ensemble since , in my notes it has only been introduced as a quantum...

Homework Statement A wheel of radius r1=0.8m and hub of radius r2=0.4m is shown in the diagram. Two masses are hung from the wheel-hub system. The mass m2, on the left, is hung from the hub. The mass m1 is hung from the wheel. The system is in equilibrium. The moment of inertia for the disk-hub...

Is there only two trusses? As shown below:

Hello everyone and happy new year. I have a quick dilemma on the concept of entanglement for a two-particle system and I am looking for some clarity: Say we have particle ##A## and particle ##B##. Both particles can be in either of the two states that we call ##|\Phi>## and ## |\beta>## or in...

Can someone please tell me how to go about optimizing this system of equations? It is weird because the residuals are computed with ##A = B*X_1+C*X_2## but X_1 and X_2 are computed in a separate function ##[X_1,X_2]=f(k1,k2,H0,G0)##, and what I am optimizing is a parameter in that second...

I'm studying Newton Raphson Method in Load Flow Studies. Book has defined Jacobian Matrix and it's order as: N + Np - 1 N = Total Number of Buses Np = Number of P-Q Buses But in solved example they've used some other formula. I'm not sure if it's right. Shouldn't order be: N + Np - 1 N = 40 Np...

Homework Statement Homework Equations If load is inductive current lags voltage. If load is capacitive voltage lags current The Attempt at a Solution Current lags voltage since wire is inductive. So IF1 lags VF1 and IF2 lags VF2 But book says answer is C Why should VF1 lag IF1? This will...

Can anyone predict where the planets will be in 1 million years time, could the Earth be kicked out of orbit a far quicker way to die than waiting for the sun to go nova?

Homework Statement A basketball with a mass of 0.56 kg drops from a height of 5 m and bounces off the floor back up to a maximum height of 4.3 m .Find the work done on the ball by the ground during the time the ball is in contact with it. Homework Equations W = - Δ Ug Ug = mgh The Attempt at a...

Consider the equation system x*e^y + y*f(z) = a x*g(x,y) +z^2 = b where f(z) and g(x,y) are differentiable functions, and a and b are constants. Suppose that the system defines x and y as differentiable functions of z. Find expressions for dx/dz and dy/dz. Any help would be appreciated...

why system has a rotational symmetry in dirac equation? is that a general property of all systems?

Homework Statement Which of the following statements is always correct? A) The work of friction force is negative. B) The work of gravity is positive C)The work of the spring is negative D) The work of the normal force is negative E) None of the above The Attempt at a Solution My answer is E...

"There are various theories about how the solar system formed, but scientists haven't been able to agree on a single model that explains all the quirks of our corner of space as it exists today. Now, scientists at the University of Chicago have...

Hello, Suppose we humans traveled in a spacecraft to another Earth like planet with the same gravity and atmospheric composition as our own Earth. Suppose we landed on the surface. Suppose we opened the door of the craft, and walked onto the planet surface. Suppose we did not wear a...

Hi everyone, i'd like to share my packaged (plug and play) solar system project that I assembled at home. I used mostly standard parts such as a charge controller, inverter, 12 Volt UPS battery, and a pair of NEMA 5-15 R power outlets. I built the automatic transfer switch and battery...

My chemistry course says that work done by the system is negative, but physics course says that work done by the system is positive, I'm sure I'm missing something and I really need to understand it. Thanks.

Homework Statement Two blocks, m1 = 1.0 kg and m2 = 2.0 kg are connected by a light string as shown in the figure. If the radius of the pulley is 1.0 m and its moment of inertia is of the system is 5.0 kg*m^2, the acceleration of the system is (expressed as a fraction of gravitational...

Homework Statement A pulley with a radius of 3.0 cm and a rotational inertia of 4.5×10^-3 kg·m2 is suspended from the ceiling. A rope passes over it with a 2.0-kg block attached to one end and a 4.0-kg block attached to the other. The rope does not slip on the pulley. At any instant after the...

There are three geothermal systems that are commonly used: sry steam, flash steam, and binary cycle https://www.eia.gov/energyexplained/index.cfm?page=geothermal_power_plants . What are the efficiencies of the plants from best to least effecient on average?

Hello and thanks for looking at this question. I have a semi-conducting sample which has been run on a PPMS system - measuring it's resistivity as a function of temperature. I switched to AC transport mode in order to measure the resistivity again while applying frequencies between 1Hz -...

We have: Period T = 4, so fundamental frequency w0 = pi/2. This question seems sooo easy. But when I use the integral: x(t) = Σa[k] * exp(i*k*pi/2*t). I get 1 + sum(cos(k*pi/2*t)), which does not converge. Where did I went wrong ? Thanks a lot for your help.

Homework Statement I am Pretty Lost with this problem...[/B] A 2.45-kg aluminum pan at 155∘C is plunged into 3.58 kg of water. If the entropy change of the system is 162 J/K, what was the initial temperature of the water? NOTE:We did not receive a Tf for the system. Homework Equations...

Hello, Suppose that the angular momentum of a system can take the values 0, 1, 2. One carries out a measurement of ##J_z## on this system. What can be said about the state of the system after the measurement? To what extent can it be perfectly certain if ##J_y## and ##J_x## do not commutate...

I think that the existence of subharmonics is also bifurcation.Is that true

Hey guys I was just studying for finals and I came across something in my textbook that either wasn't explained properly or something I just don't get. So this page explains that the coefficient of y_n[k] is A_0, which is represented by b_0/a_0, I can see that a_0 is determined by multiplying...

Hi, in the following problem, I need to find the inertia of the system. The axis of rotation passes through the center of mass ( the pink dot). I understand that I will be equal to 4(mr^2). However, I do not understand why r= 3 (6 divided by 2) and not sqrt13 ( half of the diagonal of the...

Hello, in my final project for System Control i have been stuck for some time on this following task What i cannot figure out is how to make all these condition work at the same time. When I tried designing a PD controller in sisotool or MATLAB for the i and ii part it worked but i couldn't...

What I've attempted to do is resolve vertically and horizontally: T1sin(30)+T2sinΘ+T2=9g T2cosΘ=T1cos30 After that... I'm completely stuck. Any help would be appreciated, I've spent so long on this I bet I'm just missing one simple thing. Thanks in advance

Homework Statement Homework Equations To find Ca / Rb we take Ra = 0 --- is this right? I used mason's formula P1 = -G2 G1 H1 Loop = G1, G2, -H1, -H2 Using Mason's Gain we get: Delta1 = 1 Delta = 1 - G1G2H1H2 Using Mason's Gain TF = -G1G2H1 Divided by ( 1 - G1G2H1H2) But substituting the...

Homework Statement A car of mass 1500 kg is at rest on a platform of mass 3000 kg, which is also at rest. The platform has frictionless wheels attached to its bottom. The whole system is initially at rest. The car starts to move forward at a speed of 5.0 m/s with respect to the ground...

Can the Sirius star system support physical life in any way including those that can breath carbon dioxide or other gases?

I am trying to learn GR. In two of the books on tensors, there is an example of evaluating the inertia tensor in a primed coordinate system (for example, a rotated one) from that in an unprimed coordinate system using the eqn. ##I’ = R I R^{-1}## where R is the transformation matrix and...

Homework Statement Hello! I have some problems with constructing Lagrangian for the given system: (Attached files) Homework Equations The answer should be given in the following form: L=T-U=... The Attempt at a Solution I tried to construct the Lagrangian, but I'm not sure if I did it...

In a closed fluidic system (with a pump), fluid velocity is constant throughout the system but what puzzles me is the pressure drop due to viscous effect. In a horizontal pipe, pressure decreases gradually (assuming low friction) down the pipe due to viscous effect. In this concepts, it's hard...

Homework Statement Force of 200 foot pounds of torque is being exerted on a axle of a disc which is turning at 1.57 radians. The disk has a moment of inertia of 234 kg per meter squared and it's 1.5 inch diameter axle has a prony brake installed applying a load of 200 foot pounds of torque at...

Homework Statement A system having ##N## non-degenerate energy eigenstates populated by##N## identical spin-zero particles and ##2N## identical spin-half particles. There are no interaction between any of these particles. If ##N=1000## what is the entropy of the system? Homework Equations...

Hi, I have derived a matrix from a system of ODE, and the matrix looked pretty bad at first. Then recently, I tried the Gauss elimination, followed by the exponential application on the matrix (e^[A]) and after another Gauss elimination, it turned "down" to the Identity matrix. This is awfully...

Homework Statement Steam is expanded from 90 bar, 412°C to 4.0 bar saturation in a high pressure turbine, after-which a certain percentage of the steam is bled off to a feed heater. The remaining steam is then expanded through a low pressure turbine to 1.0 bar and dryness fraction of 0.93. All...

I'm working on my first engineering project in the real-world and I'm hitting a bit of a snag. It's regarding pressure loss analysis in an HVAC system. We have a system that is capable of providing a maximum of 2.0-in.wg pressure at the air handler, but we are finding very little air movement at...

For the structure, find the distance from O (in direction OA) to the point where the resultant force-couple system of the forces shown should have a resultant couple of zero. Give answer in metres. a=90 N, b=289 N, c=549 N Clockwise negative, anticlockwise positive. Moment at a =...

Suppose the polynomial p has all its zeros in the closed half-plane $Re w\le0$, and any zeros that lie on the imaginary axis are of order one. $$p(z)=det(zI-A),$$ where I is the n x n identity matrix. Show that any solution of the system $$\dot{x}=Ax+b$$ remains bounded as $t\to{\infty}$...

Homework Statement Hello, I am attempting to use the velocity Verlet algorithm of integration applied to the solar system in c++. My goal is be able to use the outputted position components in a plot to see if the trajectory of my object is elliptical/parabolic/hyperbolic resulting from the...

1. Derive the wave equation for longitudinal vibrations in an extended 1-D system of masses and springs. The average distance between masses is D [m], the spring constants are K [kg/s2 ], and the masses are M [kg]. b) Determine the wave speed c as a function of D, K, and M. Verify that it has...

Homework Statement Consider the center of mass system of two interacting fermions with spin 1/2. a) What is the consequence of the Pauli exclusion principle on the two-particle wave function? b)Let S1 and S2 be the spin operators of the two individual fermions. Show that the operators...

Homework Statement [/B]A quantum system has three energy levels, ##-0.12 ~\rm{eV}##, ##-0.20 ~\rm{eV}## and ##-0.44 ~\rm{eV}## respectively. Three electrons are distributed among these three levels. At a temperature of ##1727^o \rm{C}## the system has total energy ##-0.68 ~\rm{eV}##. What is...

Vibrations - Modelling system, equation of motion Hi, In the first question (question 4) in the attached file, how would you go about modelling the system and finding the equation of motion? All those masses are confusing me, I don't even know where to start. I don't know whether the angle...

Homework Statement 173 g of water at 20°C is contained in a copper container of mass 327 g. An additional 129 g of water at 100°C is added. What is the final equilibrium temperature (in degrees C) if we treat the system's water and container as isolated? Homework Equations Q = mcΔT The...

Hi! I'm doing a research project titled "Is it possible to colonise Mars?" I'm currently researching how to raise the temperature and pressure - and I've discovered to do this that re-directing asteroids towards Mars containing Ammonia would be vital. However, where do these asteroids that...