Layers not overlapping in QGIS?
Mis-aligned shapefiles in QGIS?
Why don't I get $e$ when I solve $\lim_{n\to \infty}(1 + \frac{1}{n})^n$? Move post to different user The equivalent electric field of a magnetic field I know that Lorentz force for a charge $q$, with velocity $\vec{v}$ in magnetic field $\vec{B}$ is given by  $$\vec{F} =q \vec{v} \times \vec{B}$$  but there will exist a frame of reference where observer move at same velocity with that of charge $q$, so according to him $v=0$. hence he will see no magnetic force is exerted on charge $q$. I have work on this problem for a while and found that the special relativity predicts equivalent electric force will acting upon charge instead. I want to know the relationship between this equivalent electric force and magnetic force.  Thanks in advance Proving the two given vectors are orthogonal I am given the vectors $\mathbf{w}, \mathbf{v}, \mathbf{u}$ in $\mathbb{R}^n$ such that $\mathbf{u} \neq 0$ and $\mathbf{w} = \mathbf{v} - \frac{\mathbf{u}\,\bullet\,\mathbf{v}}{\|\mathbf{u}\|^2}\bullet\mathbf{u}$. I am asked to show that the vector $\mathbf{w}$ is orthogonal to $\mathbf{u}$.     So far, I have written out the definition of orthogonal: two vectors are orthogonal if and only if their dot product is zero.   So what we need to prove is $\mathbf{w}\bullet\mathbf{u} = 0$ where $\mathbf{w}\bullet\mathbf{u}$ is defined as $\mathbf{w}^T\bullet\mathbf{u}$.   However, I have been stuck on this problem for about an hour and haven't made any significant progress from here. How do we go about proving that the vectors are orthogonal? I am just starting into calculus and I have a question about the following statement I encountered while learning about definite integrals:  $$\sum_{k=1}^n k^2 = \frac{n(n+1)(2n+1)}{6}$$  I really have no idea why this statement is true. Can someone please explain why this is true and if possible show how to arrive at one given the other? Does leaning (banking) help cause turning on a bicycle? Why am I getting strange results when using a power meter to measure CFLs? How can I change some pages into document into landscape mode, while leaving the others in portrait mode (or vice versa)? This is a question from my proofs course review list that I have had trouble understanding.   I understand the concept of disjoint sets.  I'm not sure what they mean by countable. How would one prove a set is countable and furthermore, that the union of two countable sets is countable.  Please help me get started with the question by understanding this concept. MWE:  \documentclass[a4paper,12pt,twoside]{memoir} \usepackage{DejaVuSerifCondensed} \usepackage[T1]{fontenc} \begin{document} \noindent\scshape{Hello World}\\ \textsc{Hello World} \end{document}   Explanation and question:  As you can see, I am working with a memoir document class and I've load a font DejaVuSerifCondensed, I am trying to obtain small caps for my header (which I did not place in the MWE as unnecessary). However I can't obtain the desire effect with the \scshape command nor with the \textsc{}.  I've seen other questions like     .   But either they do not adapt to my problem (for what I can see) or they do not solve the problem (following the instructions there and "inserting" the piece of code in mine).  Question here is: is there a general method (piece of code or something) to obtain small caps from a custom font (even if that is one I upload with a ttf)?, if not, what would be the piece of code to select the standard small caps font? "All of the ...." or " All the ... "? Can I configure Ubuntu to never install a specific package even if it is required by another package I install? How would you explain JavaScript closures to someone with a knowledge of the concepts they consist of (for example functions, variables and the like), but does not understand closures themselves?  I have seen  given on Wikipedia, but unfortunately it did not help. Skyrim crashes as soon as I boot up into the menu. How do I fix this? Whenever I boot up Skyrim, it crashes as soon as it reaches the main menu with no dialog or anything. I thought this was related to my using dual monitors somehow, but I disconnected the other monitor and the game still crashed. I tried running the game in different resolutions, both full-screen and windowed, at various quality settings; no dice. My computer does meet the minimum requirements to play Skyrim.  How do I fix this problem? Why separation of variables works in PDEs? Find $\,\lim_{x\to 1}\frac{\sqrt[n]{x}-1}{\sqrt[m]{x}-1}$ Unable to uninstall Wine apps Why is polyploidy lethal for some organisms while for others is not? Approximation of real number to the power of irrational Say I have two numbers, $c\in\Bbb R^+\,,q\in\Bbb{R\setminus Q}$.  Is there a way to approximate the value of $c^q$?  This question bugging me because of how simple it sound in compare to how complicated it is. First I want to understand what a power of irrational number is, when talking about $\Bbb R^+$(I use this domain for sake of simplicity) we have very well defined actions for power a rational number, we can even use some theorems to get $c^{a/b}=\sqrt[b]{c^a}$, but when I am dealing with irrational number I can not do this.  I know that we have some definition for this because the solution of the equation $2^x=3$ is irrational.  So what exactly does it mean to take something to a irrational power and is there a way to approximate a numeric value for this? I took this photo of the blood moon this morning and I am finding many of my photos, especially landscape photos, have a significant lack of clarity. I'm not looking for a photo critique because I know this particular photo is crap. I'm looking to identify my source of failure to nail a significantly clear photo.     Setup  Canon EOS 70D with a 100-300 telephoto lens (I'm sorry I don't know the exact model. It's from Canon but not one of their professional quality lenses.)   Aperture: f/5.6 Shutter: 1 sec. ISO: 1000 Focal Length: 300mm Metering mode: Spot White Balance: I manually set the WB to 5500 kelvin, it looked fine in live view. Focus Mode: Manual Drive: 2 sec timer delay   Mounted on a decently stable tripod  Process  I turn on live view, and square up the target in the display. I then set my focal length, focus in using live view, adjust the focus as sharp as possible and take the pic. I've noticed that in this case, the picture was incredibly grainy, which doesn't translate to the final photo, but wonder if it has anything to do with it.  This particular shoot I found it difficult to balance out the variables with a dark sky and a moving moon that starts blurring after 1-2 seconds of exposure, which is why I had the aperture wide open and the ISO cranked up.  I can't tell where I'm failing:  Equipment:  The 70d takes great photos but the telephoto is not great when it's totally zoomed in. My wallet doesn't hold enough cash for a motorized mount to track objects in the sky.  Circumstance: I've seen great photos of the moon with the use of a camera and a tripod, so I know this is possible. Although, I keep seeing pictures of this big gorgeous moon over the landscape, and when I use my wide-angle, the moon shows up as a dot. What the hell are people doing to get the moon so big?  Beginner skill level: I know this is the biggest culprit, but being the beginner, I'm unable to know where to adjust.