Unit Definition and 1000 Threads

Hey! :giggle: Let $\lambda\in \mathbb{R}$ and \begin{equation*}a=\begin{pmatrix}1 & 2 &-1& \lambda & -\lambda \\ 0 & 1 & -1& \lambda & 2\\ 2 & 2 & 1 & 1 & 3\lambda-1 \\ 1 & 1 & 1 & \lambda & 5\end{pmatrix}\in \mathbb{R}^{4\times 5}\end{equation*} (a) Let $\lambda=1$. Determine a Basis...

In my textbook it is given that Molarity is represented by M, and its formula is-- Molarity(M)= No. of moles of solute/Volume of solution in L the unit of Molarity is mol/l which is also written as M. Now what does this mean ? does it mean --> Molarity is denoted by "M" and it's unit is also...

First of all, I don't think the question was clear enough. Therefore, I had to assume they are referring to the volume of the unit cell. V=a^3, side length a aBCC=2R√2, aFCC=4√3/3R %change=(VFCC-VBCC)/VBCC I thought this was right until I checked with others who did this: so the only...

\begin{equation} \chi = n \sigma \end{equation} Where Chi is the Opacity, n is the number density of absorbers (constant), and $\sigma$ is the cross section(given). We define the optical depth is just the number of photon mean-free paths in a given physical step, i.e. if we consider a...

I have worked out (and then verified against some sources) that ##R^\theta_{\phi\theta\phi} = sin^2(\theta)##. The rest of the components are either zero or the same as ##R^\theta_{\phi\theta\phi} ## some with the sign flipped. I was surprised at this, because it implies that the curvature...

I'm having difficulties solving this. For finding a unit vector that is orthogonal to two unit vectors I understand we use the cross product and such. However, I am confused about how to approach this problem as it has a third vector. We can let x = (x1, x2, x3, x4) be a vector orthogonal to u...

If we use the nature units or the geometrized units, how could we transfer the final result back to the normal units with ##c \ne 1, \hbar \ne 1, G \ne 1##? I know I coule analysis its dimension to multiply them back. But what about other units system? For example, in a recent paper, the...

I just wrote down what I think and have no idea of it...please help me with this question

relevant equations: My questions: (1)Not sure whether I did correct especially for the deflection angle (2)The limit taken for calculating defection Yc , I didn't understand why is from 0 to L/2 instead of the sum of 0 to L/2 and 0 to L, how is the limit determined? Kindly advise, thanks

New to electricity so take it easy on me... I have a light unit: 14 VDC @ 3.2A / 28VDC@ 1.6A 2 questions: I was curious to see if a 9V Duracell battery will power it up: and it turned it on but I noticed my battery head bubbled up. From my understanding correct me if I am wrong on a 9V...

Writing both ##\vec{U}## and ##\vec{B}## with magnitude in all the three spatial coordinates: $$ \vec{U}\times \vec{B}= (U_{x}\cdot \widehat{i}+U_{y}\cdot \widehat{j}+U_{z}\cdot \widehat{k})\times (B_{x}\cdot \widehat{i}+B_{y}\cdot \widehat{j}+B_{z}\cdot \widehat{k})$$ From this point on, I...

I don't understand the ratio [ 1 g / 6.02*10^23 amu] in the following conversion factor: [228.2 amu / 4.75*10^(-23) cm3] * [ 1 g / 6.02*10^23 amu] = 7.98 g/cm3 (This calculation is in a problem where you're finding the density of a unit cell in g/cm3 - though it has nothing to do with the...

This is actually right at the start of another derivation, but I can't understand how the author gets the formula for ##q##. So the discharge per unit thickness is the circumference of the circle, multiplied by the velocity at that point (at ##r##)? I thought the formula for flow rate was...

If there is a luminosity per unit wavelength defined as L_λ dλ, am I correct in thinking that the conversion to luminosity per unit frequency (L_ν) would be L_ν = L_λ (λ^2/c)? And building off of that, if the shape of a spectrum was proportional to a power-law: L_λ = λ^(β), is there a way to...

Why is it that the radius of the unit circle is 1?

what means unit j.s in plank constant As Planck's constant is the smallest unit of energy so what this unit j.s

Find point d on the line of r(t)=(0,0,0)+(−1,1,1)t which make the triangular pyramid abcd has the volume of 4 unit cube when a(0,0,0),b(1,0,1),c(0,1,0) are the points on the plane of −x+z=0.

Hi guys, I used to post on here quite a bit back in 2005-2007 when I was studying Physics in school, I remember it always being a great resource so hopefully I can get some similar help with this "real life" problem I'm having now! We are having a mini-heatwave here in the UK the last few...

I'm modelling the interiors of core-dominated (exo)planets. The EoS I use in my calculations are mostly either a Birch-Murnaghan formulation or a Mie-Grüneisen-Debye formulation. In either case, the ambient density ρ0 at ambient pressure and temperature are required for the implementation...

Can the unit interval be split into two measurable sets (A and B each measure 1/2), so that for any sub-interval [c,d] the intersections ##A\cap [c,d]## and ##B\cap [c,d]## each measure half the length of [c,d]? I doubt it, but I would like to see a proof, one way or the other.

James Clerk Maxwell deduced that the unit of mass has the dimensions of (L^3)(T^-2). But he assumed Newton's Law. What would it be under general relativity?

By using PV=nRT formula, I have found the volume of the vessel. As far as I have learned to calculate the number of collision in a unit volume. So, it is being difficult for me to find the right way to solve. I searched on the internet and have got this...

A unit vector, ##\frac{\vec{v}}{|\vec{v}|}##, has dimensions of ##\frac{L}{L} = 1##, i.e. it is dimensionless. It has magnitude of 1, no units. For a physical coordinate system, the coordinate functions ##x^i## have some units of length, e.g. ##\vec{x} = (3\text{cm})\hat{x}_1 +...

but the real answer is −1, (1±i√3)/2 What's wrong with my solution? please help me through.

Hi, I was trying to find the magnitude of DC signal in a shifted unit pulse signal. The unshifted pulse lasts from -π to π and then it is shifted by π duration. In Method #1 I have used FT formula and ended up with magnitude of 6.2832 for DC signal, i.e. ω=0. In Method #2 I have used Laplace...

Hi I am a beginner in this topic. I didn't understand this question type clearly.What does it mean" With Magnitude and Unit Vectors" exactly? May you help me for the solution step by step :). Thanks in advance.

How do I get the wave dispersion for a 2D continuum unit cell subjected to a periodic boundary which is excited longitudinally? I'll be applying forces in ABAQUS with varying frequencies. I have come across Blochs theorem but I can't find any application of it in continuous systems. Every...

I'm finding it slightly tricky to just get a hold of where to start. I try $$\text{m}\text{s}^{-1} = \frac{c}{3\times 10^8}$$ If we then set ##c = 1##, that would seem to imply $$3\times 10^8 = \text{s}\text{m}^{-1}$$For ##G = 1##, I might also write $$\text{kg}\text{m}^{-3}\text{s}^{2} =...

When we talk about engines on automotive industry (cars, motorbikes, trucks, etc.), we often refer the power produced by such engines by horsepower. But when we talk about electricity, the power is measured in kilowatts. Despite the former case is highly popular, why isn't horsepower considered...

I need a mapping from the unit Hypercube ##C^n:= \left[ 0,1\right] ^n## to a given simplex, namely ##S^n:=\left\{ \vec{x} \in\mathbb{R}^n |0\leq x_1\leq 1, 0\leq x_{k}\leq x_{k-1}\text{ for } k=2,3,\ldots , n\right\}##. Anybody know one? I have other requirements I need satisfy, so if you know...

Homework Statement:: None. This is part of implementing a project and not an actual question. It's a technical problem or equipment failure. Relevant Equations:: The Code I get is; Error: (vlog-7) Failed to open design unit file "Waveform.vwf.vt" in read mode. [Mentor Note -- moved to the...

Hi all, The power factor correction unit for one of the buildings that I am working on needs maintenance. The service report recommends replacing the existing 25 kVAr unit with 2 x 12.5 kVAr units as "the demand on your site according to the data supplied shows us that at most there is only...

"a charge smaller than e has not been found. if one determines the amount of charge on any charged body like a charged sphere or charged drop) or any charged particle (like positron, a-particle) or any ion, then its charge is always found to be an integral multiple of e, i.e., e,3e; 4e,... No...

Summary:: Pascal units digits Do somebody have a chart that converts pascals , mega pascals etc to units to know how many digits or zeros there are after the point please ? Thanks

1. Kelvin - not the basic, but the derived unit of measurement? Modern physics believes that kelvin is the basic unit of measurement of SI (one of seven). At the same time, in all encyclopedias and textbooks it is written: T= Θ/k = Θ /1,380649x10е-23 Θ - is the energy of the molecule in...

I tried solving the differential equation by integrating both sides wrt t but this does not work out and I am doing something wrong. How do I integrate such an equation properly? d²x/dt² = -k²/x³ => dx/dt = -k²t/x³ => x = -k²t²/2x³ + d

Hello all I am trying to find the hydrostatic force of a cylindrical tank of water. I was hoping someone could help point me in the right direction. I have a cylindrical water tank. The dimensions are as follows:- I need to find the magnitude of the hydro static force per unit of...

Hi, I am working on a kalman filter where my measurement equation involves "-g + v" , where g is in m/s^2 and v is velocity random walk given in m/s/sqrt(hr). Feels like a stupid question, but how can I transform the unit of velocity random walk so I can do the calculation correctly?

A container of height 3m and width 5m is filled with water upto 2 m. It is accelerated such that the water is at the brim (it is about to spill). When it moves with this acceleration find the force acting per unit width on the vertical wall. I found the acceleration for the condition provided...

So I'm trying to figure out the integral of phi hat with respect to phi in cylindrical coordinates. My assumption was that the unit vector would just pass through my integral... is that correct? (I reached this point in life without ever thinking about how vectors go through integrals, and...

Hello This is a really silly question but I have doubted myself and I was wondering if anyone could help. I have been given the following information:-I am trying to understand what it means when the title states Unit Weights? I thought these were density but density is kg/m^3 - whereas these...

Summary: Meaning of each member being a unit vector, and how the products of each tensor can be averaged. Hello! I am struggling with understanding the meaning of "each member is a unit vector": I can see that N would represent the number of samples, and the pointy bracket represents an...

I see various graphs in papers about atomic collisions in units showing "keV/amu". Why is this unit used, why not just "keV" when, presumably, it is the overall keV of an atomic collision that is important?

Homework Statement: Hallo. Can somebody explain to me what's the importance-use of unit vector in the below (second) equation? Why isn't the first equation just enough to describe r? What's the reason for unit vector to even exist? Homework Equations: in the photos

I'm currently researching if I could implement some wave energy into my small scale hypothetical project. I've identified some commercial models, namely Seabased and SINNPower, and I assumed that they would have approximate values of power output given wave period, height (among many other...

Hi guys , I want to construct a primitive unit cell for diamond, which is made of a fcc lattice and a basis of 2 carbons atoms. I know that a primitive unit cell isn't unique but the two variants I get are drastically different . As far as I can see they both include 2 whole atoms/points in the...

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Hi. I have been trying to calculate the real definite integral with limits 2π and 0 of ## 1/(k+sin2θ) ## To avoid the denominator becoming zero I know this means |k|> 1 Making the substitution ##z= e^{iθ}## eventually ends up giving me a quadratic equation in ##z^2## with 2 pairs of roots...

Hi, Although I'm using trigonometric form of Fourier transform, first I'd discuss both, exponential and trigonometric forms, for the sake of context. Now proceeding toward the main question and we would only be using trigonometric form. % file name...