How to find the velocity of a particle which has mass $m$ and energy $E$ considering the non-relativistic and the extreme relativistic limits?
The relativistic energy-momentum equation is:  $$E^2 = (pc)^2 + (mc^2)^2.$$ Also, we have $pc = Ev/c$, so we get: $$E = mc^2/(1-v^2/c^2)^{1/2}.$$  Now, accelerating a proton to near the speed of light, I get the following results for the energy of proton:  0.990000000000000   c =&gt;    0.0000000011    J =      0.01    TeV  0.999000000000000   c =&gt;    0.0000000034    J =      0.02    TeV  0.999900000000000   c =&gt;    0.0000000106    J =      0.07    TeV  0.999990000000000   c =&gt;    0.0000000336    J =      0.21    TeV  0.999999000000000   c =&gt;    0.0000001063    J =      0.66    TeV  0.999999900000000   c =&gt;    0.0000003361    J =      2.10    TeV  0.999999990000000   c =&gt;    0.0000010630    J =      6.64    TeV 0.999999999000000   c =&gt;    0.0000033614    J =      20.98   TeV  0.999999999900000   c =&gt;    0.0000106298    J =      66.35   TeV  0.999999999990000   c =&gt;    0.0000336143    J =      209.83      TeV  0.999999999999000   c =&gt;    0.0001062989    J =      663.54      TeV  0.999999999999900   c =&gt;    0.0003360908    J =      2,097.94    TeV  0.999999999999990   c =&gt;    0.0010634026    J =      6,637.97    TeV  0.999999999999999   c =&gt;    0.0033627744    J =      20,991.10   TeV    If the LHC is accelerating protons to $7 TeV$ it means they're traveling with a speed of $0.99999999c$.  Is everything above correct?
How to set default style for arrow tips in TikZ? onClick to get the ID of the clicked button How can I install Celestia on Ubuntu 18.04.1? Like the title said, I want to install Celestia. I already downloaded the packages  and then, I tried all the things that I found on some posts (also, they're outdated, cause the last one is for Ubuntu 16.04) but nothing works.  How can I install it on Ubuntu 18.04.1? If 20 independent Bernoulli trials are carried out each with a different probability of success and therefore failure. What is the probability that exactly n of the 20 trials was successful?  Is there a better way of calculating these probabilities rather than simply summing together the combinations of success and failure probabilities? Why are there two tensions on my free body diagram? A man sits on a platform attached to a pulley and pulls himself up as shown (ignore the angle of the rope - it should be vertical). Apparently, the man/platform object has a force of 2T pulling it up. Why is it not just T?  Much appreciated! How to type en-dash and em-dash in Windows 7/8? I write blog posts, and I often need to type en-dash (–) and sometimes em-dash (—) in my blog posts. Currently I keep these characters saved in a text file, and copy-paste them whenever I need them. Unnecessary to say, it is a headache to move between keyboard and mouse when you type large texts.  It would be better for me if there ware a keyboard shortcuts available for these two characters. Is there a way to type en-dash and em-dash in Windows? I use Windows 7 and Windows 8 in different computers.    Here's an aligned comparison of dashes, if you need to see the difference for some reason.   Here's-dash Here's–en-dash Here's—em-dash "The thing is, is that..." On the  blog post, nearly all the images are broken. I assume this is because they are all hosted on stackoverflow.blog/wp-content/uploads/ rather than zgab33vy595fw5zq-zippykid.netdna-ssl.com/wp-content/uploads/, and they got destroyed in the removal of Blog Overflow. I looked around at a few other blog posts, and this post seems to be the only one having an issue. Let $a,b$ be positive integers such that $a\mid b^2 , b^2\mid a^3 , a^3\mid b^4 \ldots$ so on , then $a=b$? Let $a,b$ be positive integers such that $a\mid b^2 , b^2\mid a^3 , a^3\mid b^4 \ldots$ that is $a^{2n-1}\mid b^{2n} ; b^{2n}\mid a^{2n+1} , \forall n \in \mathbb Z^+$ , then is it true that $a=b$ ? Just installed Ubuntu 17.10 and it seems that the keyboard layout switching has changed its behavior.  In the previous version of Ubuntu (such as 16.04 Unity), if I have 3 different keyboard layouts (for example EN-TH-JA), hitting Super+Space would always cycle to the next layout in the same order (e.g. EN to TH to JA then back to EN).  However since Ubuntu 17.10, this is no longer the case. It cycles through the layout in the MRU (Most Recently Used) ordering. So suppose that the layout starts with EN, then I cycled to TH. Next time I hit Super+Space, it would give me EN instead of JA.   I tried to dig up and found that the culprit is the newly implemented DCONF settings inside org.gnome.desktop.input-sources and there seems to be no way to change this behavior.   So my question is: Is there a way to change this behavior to "static ordering" of keyboard layout switching?    (As a side-note, the new behavior is very bad when we have three or more layouts. Most of the time we as a user couldn't remember the MRU layouts, so layout switching is very inconvenient and much slower than already knowing what the next layout would be if static ordering is used.)  If there is no settings to change this behavior, where should I report this as a bug or a feature request? The number of different ways to choose $k$ out of $n$ unique items The number of different ways to choose $k$ out of $n$ unique items:   Without repetition and without order-significance: $\binom{n}{k}=\frac{n!}{k!(n-k)!}$ Without repetition and with order-significance: $\binom{n}{k}\times k!=\frac{n!}{(n-k)!}$ With repetition and with order-significance: $n^k$ With repetition and without order-significance: $?$   Thank you! When I try to print a Unicode string in a Windows console, I get an error . UnicodeEncodeError: 'charmap' codec can't encode character .... I assume this is because the Windows console does not accept Unicode-only characters. What's the best way around this? Is there any way I can make Python automatically print a ? instead of failing in this situation? Edit:  I'm using Python 2.5.  Note: @LasseV.Karlsen answer with the checkmark is sort of outdated (from 2008). Please use the solutions/answers/suggestions below with care!!  is more relevant as of today (6 Jan 2016). Cycles Emit Light from area on Texture So I have a giant object that is completely uv unwrapped. I would like to make areas of the object with a specific area of texture emit light.   The problem is that this object (and it is only one object) only has one material. I would like the lava to emit light, but I cannot move it to a separate material without breaking something.  I'd like to find a method where I can select a part of the texture and tell blender that whatever has that part of the texture emits light.  Is this possible?  Thanks. What is the number of automorphisms (including identity) for permutation group $S_3$ on 3 letters? What is the number of automorphisms (including identity) for permutation group $S_3$ on 3 letters?  I believe the answer for this is 6. As we can write the group elements as below   (a)(b)(C) (ab)(c) (ac)(b) (bc)(a) (abc) (bac)   Can we generalize that for any $S_n$ onto $n$ the number of automorphisms will be $n!$ Also I cannot find this anywhere in my text, can we have a permutation $S_n$ onto $m$ where $n\neq m$? (for eg: is it possible to have a permutation group say $S_5$ on say 2 elements?) How to permanently allow location access for a website in Safari 11? I have some questions regarding suspended users:   Why do suspended users have a reputation of one? According to the default reputation of a new user, he/she will have reputation of one and he/she has the privilege of posting questions. When comparing this, this is getting violated when compared to suspended users' reputation. Even though they have one reputation point, they cannot post questions. As suspended users do not have privilege of posting questions, there is no use of making "Ask Question" visible. This is an unnecessary server hit. Am I right? As suspended users do not have the privilege of answering questions, there is no use of making "Answer Question" visible. I'm buying a bus ticket to get to Boston 23 hours before my flight to ensure I reach my departure airport on time.  If I didn't arrange bus transport well in advance, what legal remedies would I have if a delayed bus caused me to miss my flight? Uncertainty principle and multiple observers My understanding is that an observer can measure the precise location of a particle so long as the corresponding uncertainty in momentum measurement is not an issue and vice-versa.    Say there is such an observer, interested in the precise position of a particular particle.  Now, consider a second, independent observer, unbeknownst to the first, who is trying to measure the exact momentum of the same particle without caring about the position.  As a thought experiment, we assume that the two observers are somehow able to access the same particle at the same time in some way without being aware of each other.  Can both observers get their desired results? How to create csv files in controller method from list I want to create csv files from lists and send an email attaching them, how to do that in a controller method? every eigenvalue of $T$ has only one corresponding eigenvector up to a scalar multiplication For a linear transformation $T$ on a vector space $V$ of dimension $n .$ Suppose it is given that for some vector $\mathbf{v},$ the vectors $\mathbf{v}, T(\mathbf{v}), T^{2}(\mathbf{v}), \ldots, T^{n-1}(\mathbf{v})$ are linearly independent, then is it true that every eigenvalue of $T$ has only one corresponding eigenvector up to a scalar multiplication.