I'm a high school student and I'm fairly familiar with basic electronics, but I've always wondered one thing.  So how generators make electricity from motion is the move a magnet around or through a coil of conductive wire,  which causes the electrons from the metal to move in the direction of the magnet. But that could theoretically happen forever. When does the metal wire run out of electrons? Are electrons being formed? Is matter being created?   Also if you want to help me out a bit more, please explain how transformers work and how voltage and amperage are related.
Where do the electrons come from when an electric generator is making electricity?  Is from the air?  Would a generator work in a vacuum?  Electrons have mass so where would they be pulled from if there is nothing?
Visual design changes to the review queues A novel where a woman from "future" of 1999 speaks leet-speak I'm trying to remember the name of a novel/series I read back in the mid-eighties.  I can't remember the author other than that it was a known older author.  I initially thought maybe Saberhagen or Harrison, but can't find it in their bibliographies.  It involved a collection of 4-5 people from different times/places.  The distinctive bit I can remember was that one of them (not the main character) was a cyberpunkish woman from the "future" of 1999 who spoke in futuristic dialect of English that the other characters, including the protagonist, from the "present" (from the eighties) could not understand.  Unfortunately, I don't remember much else of the plot other than that they were making their way through ruins. Finding a tricky limit I have a homework in real analysis and I'm very confused about it. I would be very thankful, if you could give me any ideas or solutions how to get this task done. The task is as follows:     Find the limit:   $$\lim_{x\to 0} \frac{1}{x} \int_{0}^{x} (1+ \sin(t))^{1/t} dt.$$   A hint that has been given is to use L'Hospital's Rule. Moreover, it must be substantiated why we can use L'Hospital' Rule in this situation. It is also important to mention that $(1 + \sin(t))$ has a removable point of discontinuity at $0$ and therefore the integral can be interpreted as a Riemann integral. Can't find wifi drivers for 0bda:f179 Realtek Semiconductor Corp I'm trying to install wifi drivers for a particular mini wifi card i bought. The output of lsusb is:  0bda:f179 Realtek Semiconductor Corp   I've searched everywhere for drivers, but could not find anything. Any help?  Thanks The error message is :the grub-efi-amd64-signed package failed to install into /target/. Without the GRUB bootloader the system will not boot  I'm trying to install on HP pavilion g6-2303 TX using USB.  How do I fix this problem? Ksplice is an amazing software (or whatever it is). It changes the way kernel updates work: Instead of rebooting after an update, it patches memory, so you don't need to do anything. Let $X,Y,Z$ be subspaces of $V$ so that $X$ is a subspace of $Y$. Prove that $Y\cap (X+Z)=X+(Y\cap Z)$ Let $X,Y,Z$ be subspaces of $V$ so that $X$ is a subspace of $Y$. Prove that $Y\cap (X+Z)=X+(Y\cap Z)$  I know that I need to prove that $Y\cap (X+Z)\subseteq X+(Y\cap Z)$ and $X+(Y\cap Z)\subseteq Y\cap (X+Z)$ but I´m having a hard time.  Can you lend me a hand please? I would really appreciate it I am trying to add a timed delay in a C++ program, and was wondering if anyone has any suggestions on what I can try or information I can look at?  I wish I had more details on how I am implementing this timed delay, but until I have more information on how to add a timed delay I am not sure on how I should even attempt to implement this. Repeat copies of array elements: Run-length decoding in MATLAB Quoted vs unquoted string expansion TTY doesn't wait for password I upgraded from 16.04 to 18.04. When I press Ctrl+Alt+F3 I get the terminal which prompts for the username. When I type my username and press Enter, it doesn't wait for my password (its as if I pressed Enter without entering anything). Even if I enter something, the text shown in plaintext and then it keeps on saying my password is wrong. After few times, the screen is cleared and it prompts for my username again and the same loop goes on. Goofy looking alien robots lose a "Kleptonite Ball" towed behind their spacecraft Can two people with different one time pads securely exchange a message like this? Alice has a message, generates a one time pad, encrypts her message and sends it to Bob. Bob generates his own one time pad, encrypts the message again, and sends it back to Alice. Alice then decrypts this message using her one time pad, sends it back to Bob who then decrypts it the last time using his one time pad.  The only problems I see with this technique:   It is vulnerable to a man in the middle attack. It requires sending the message back and forth twice between sender and recipient. It doesn't scale well if you want to use it to communicate with multiple people. Requires a way of generating cryptographically secure random numbers.   Does this method of encryption have a name?  If we ignore the fact that it's vulnerable to a man in the middle attack, is this method of encryption information-theoretically secure?  Why isn't this method used widely, i.e. which of the above listed problems or other problems makes this method infeasible for production use? Badass and BAMF are both modern words with approximately the same meaning: "Someone who is awesome to an extreme level, thereby leveraging unquestionable authority." Is there another noun or title that would convey the same level of awe, admiration and toughness that calling someone a badass does, without the vulgarity?  Thanks for any help. :) Let $n$ be a nonnegative integer, and $k$ a positive integer. Could someone explain to me why the identity $$ \sum_{i=0}^n\binom{i+k-1}{k-1}=\binom{n+k}{k} $$ holds? How to install import_3dm add-on properly? Why is "glide symmetry" its own type? Artin's Algebra pages 155 &amp; 156 list the types of symmetry of a plane figure as:   Reflective Rotational Translational Glide   He then goes on to say "Figures such as wallpaper patterns may have two talk about other figures having combinations of independent" symmetries. EDIT: He says "... having combinations of independent translational symmetries". See Joriki's answer.  Why doesn't glide symmetry count as having two independent (reflection + translation) symmetries? If we're going to count combinations, why not have rotation + translation etc. as their own types too? Can I install any iOS version I wish by picking and choosing which firmware to restore? I'm trying to downgrade my iPhone from the current iOS to an older one, as per .  But every time I try, I always receive this error:     The iPhone could not be restored. This device isn't eligible for the requested build.     I have tried many times with and without DFU mode. Any ideas regarding this? Primary ideals of $\mathbb{Z}$ Let $R=\mathbb{Z}$ I must prove that      In $\mathbb{Z}$ the primary ideals s are precisely the ideals $(p^k)$ where $p$ is a prime number and $n\ge 1$.   $$$$ The definition of primary ideal.     Definition. An ideal $I$ of the ring $R$ is called primary if for all $a,b\in R$ $$(ab\in I\quad\text{and}\quad a\notin I)\Rightarrow b^n\in I, \text{for some positive integer $n$}.$$   Therefore I must prove that      $$(n)\;\text{is primary in}\;\mathbb{Z}\iff n=p^k, k\ge1,p\ge2,\;\text{where}\;p\;\text{is a prime}.$$   Proof ($\Leftarrow$) We suppose that $n=p^k$ for same prime $p$ and $k\ge 1$. Let $a,b\in\mathbb{Z}$ such that $ab\in(p^k)$ and $a\notin (p^k)$. Then $p^k\nmid a$, but $p^k \mid ab$ I no longer know how to proceed.  $(\Rightarrow)$ Let $(n)$ a primary ideal and we suppose for absurd that $n$ is not a power of a prime, then? how could I proceed?  Now, let $ab\in (p^k)$ with $a\notin(p^k)$, then $p^k\mid ab.$ Can I conclude that $p^k\mid b$?   How can I set up the other implication? Thanks Huawei E3272 Ubuntu I have a problem with Huawei E3272 modem. Ubuntu 14.04 does not detect it as a mobile broadband modem. If I put my SIM card into my old modem(E3131) everything works, E3272 is just not detected. I have checked lsusb, and here I can see the system detects it as  12d1:14fe Huawei Technologies Co., Ltd.  but I cannot choose it in my Network Connections.  I tried adding usbserial vendor=0x12d1 product=0x14fe in /etc/modules, but it did not change anything. The same goes for adding   # Huawei E3272  ATTR{idVendor}=="12d1", ATTR{idProduct}=="157c", RUN +="usb_modeswitch '%b/%k'"  in /lib/udev/rules.d/40-usb_modeswitch.rules. I also tried installing Modem Manager, but it did not help.  Have you got any idea what could I do, so my system would detect my new modem? I would like to be able to use LTE. :)