Scale a tikz picture
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How do I see that every left ideal of a square matrix ring over a field is principal? As the question title suggests, how do I see that every left ideal of a square matrix ring over a field is principal? We're building a feature for a website and trying to think of a hypernym for clients, partners and members so that the feature remains generic enough for re-use later on other websites. I find it funny that Java (or the java.util library) does not have a built-in function to calculate difference in dates. I want to subtract one date from another to get the elapsed time between them. What is the best way to do this?   I know the simple way is to take the difference of the time in milliseconds and then convert that into days. However, I wanted to know if this works in all cases (with daylight saving, etc.). Proving a direct product of groups is a group I am trying to prove the following and am looking toward the math.stackexchange community to comment on whether I am on the right track or not. Thank you in advance.    Let $n \geq 1$ be an integer. Suppose $\{G_1,...,G_n\}$ is a finite set of groups. Define the set $G = G_1 \times G_2 \times ... \times G_n$ of ordered n-tuples $(g_1,g_2,...,g_n)$ where $g_i \in G_i$. Show that the operation $\bullet$: $G \times G \rightarrow G$ given by $(g_1,g_2,...,g_n) \bullet (g'_1,g'_2,...,g'_n) = (g_1g'_1,g_2g'_2,...,g_ng'_n)$ makes $G$ into a group.    Proof of associativity: $((g_1,g_2,...,g_n) \bullet (g'_1,g'_2,...g'_n)) \bullet (g''_1,g''_2,...,g''_n)$ = $(g_1g'_1,g_2g'_2,...,g_ng'_n) \bullet (g''_1,g''_2,...,g''_n) $ = $(g_1g'_1g''_1,g_2g'_2g''_2,...,g_ng'_ng''_n)$ = $(g_1,g_2,...,g_n) \bullet (g'_1g''_1,g'_2g''_2,...,g'_ng''_n) = (g_1,g_2,...,g_n) \bullet ((g'_1,g'_2,...,g'_n) \bullet (g''_1,g''_2,...,g''_n))$  \  Proof of the existence of an identity For each $G_i \in G$, take its identity element $e_i$ and multiply it as follows: $(g_1,g_2,...,g_n) \bullet (e_1,e_2,...,e_3)$ = $(g_1,g_2,...,g_n)$.  \  Proof of the existence of an inverse: Since each $G_i \in G$ is a group, simply takes its multiplicative inverse $g_i^{-1}$ and multiply it: $(g_1,g_2,...,g_n) \bullet (g_1^{-1},g_2^{-1},...,g_n^{-1}) = (e_1,e_2,...,e_n)$. How does editing work? It is possible for users to edit an existing post.   How do edits work? Who may edit a question or answer? How can you tell what has been changed between edits?      For more information, see "" in the .     Related: this circuit is a occupancy light circuit i want to know the working of the transistor regarding base,collector and emitter in the transitor " could " vs. " could have " As I know we can use both structures to talk about past ability , but is there any difference between them?  A. He could climb the mountain  B. He could have climbed the mountain How can I search an Excel spreadsheet in SharePoint? Looking to be able to search an Excel spreadsheet from the SharePoint mobile app.  I have a spreadsheet with Postal Codes/Zip Codes with corresponding information. I would like to be able to search as you would in Excel.  When I upload a test spreadsheet, it opens as like a PDF. User has "Read" permissions for the document library the spreadsheet is located in.  Thanks in advance, How to delete pre-installed apps in Catalina? I want to delete the pre-installed apps, like Music, Books, Siri etc. from my iMac running Catalina. How do I do this?  (NOTE:  asks the same thing but was closed as a duplicate of . Annoyingly, the supposed duplicate doesn’t give an obvious answer to the question, and the original was locked can’t be answered, hence a new question. I can’t add an answer to  either) From :  Error propagation It was common to discuss the &quot;error propagation&quot; properties as a selection criterion for a mode of operation. It might be observed, for example, that a one-block error in the transmitted ciphertext would result in a one-block error in the reconstructed plaintext for ECB mode encryption, while in CBC mode such an error would affect two blocks.  I read  similar post before. And I can understand that in CBC decryption, only two blocks are affected due to error propagation (error in 1 block). But, for the same case in CBC encryption, why are still only two blocks affected? It looks like all the following blocks will be affected. Is it acceptable to change colors on a logo to make it fit a website's theme? I have a few payment brand images that need to go in the footer of a website, the footer is very dark grey, to the point where making the logos grey-scale wouldn't be much of a good idea, especially as we still need the logos to stand out.  For example I took the following logo:   And changed it to fit with our very dominant red theme:    Is this good in terms of the user's perspective? Is this legal or misrepresenting the brand? If so is completely changing a logo to white acceptable for dark backgrounds? After the  of registering an account to book train tickets online using my British VISA card, I finally got into a position of being able to book a ticket, but what it appears to be telling me is that I'm only being added to a wait list, which I assume means my tickets aren't confirmed.  Can someone explain how the wait list works, and what my chances are of getting on the train successfully?    It currently says the wait list is 7 The train is the Mandor Express, from Delhi to Jodhpur on the 18th of Nov   Update: So I got the train! Although it didn't get confirmed until a few hours before it was due to leave. I’ve always understood that the phrase two weeks usually turns into two weeks’ when used as a modifier as in   I’m giving my two weeks’ notice.  I get two weeks’ vacation. (“two weeks’ holiday” for Brits)   with an apostrophe on the word weeks’, indicating that the vacation “belongs” to the weeks.   One way to explain this is the phrase “two weeks of vacation” being contracted to “two weeks’ vacation” – the vacation is “of” the weeks; that is, it is possessed by them.  But I’ve seen a lot of people omit the apostrophe in casual writing, and thinking about it, it seems plausible that the noun vacation would be plainly modified by the adjectival phrase two weeks.  But on the other hand, shouldn’t adjectival phrases be hypenated, namely two-weeks vacation?  Yet that seems wrong, too: the hyphenate should be singular, two-week vacation (like two-tone shoes) because .   touches on this (and references a good ) but doesn’t explain why the plural must be possessive in this case.   suggests that two weeks might be adverbial rather than adjectival, and thus resists being used attributively. But that still doesn’t quite explain this particular muddle of pluralization, possession, and attribution.  Given all this, why should “two weeks vacation” be written “two weeks’ vacation” with a possessive apostrophe? What is a good package for displaying algorithms? I found this page with some examples:   I'm wondering which one to use. Any suggestions? I'm using other packages too so whichever is less likely to interfere with them is better for me. What is the LaTeX command for "em dash" (—)? I am trying to insert the symbol in the title of the question, which I copied from a PDF article, but it appears as space in the output file. What is the corresponding LaTeX command? How can I find unanswered questions with zero answers in some tag? Electrical outlet on a dimmer switch? I live in an older house and have some outlets in our kitchen that don't make sense to me. We have one outlet that is tied to a dimmer switch on the opposite side of the room. I can detect that the outlet is hot using my voltage detector (when the dimmer switch is all the way on), but it pulses. I get about 6-7 beeps, then it skips one, beeps 6-7 more times, skips, continue. My GFCI tester shows an open hot. The outlet doesn't work.  I'm not very experienced with electrical work but this sounds highly unusual to me. Where should I start with fixing the issue? How do I get query string value from script path? I don't follow understand what this theorem is saying: "Every function $f: A \to{\cal P}(A)$ is not surjective."   Is this saying so for example let A = {1,2,3} then the power set of A is {},{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3} Is this saying that there is no surjective function that takes every element in each of its power sets to atleast 1 element in A?  Is my understanding correct? How to get dialog box input directed to a variable? I have been teaching myself bash scripting and have run into an issue. I have written a script to take input from the user, using the 'read' command, and make that input a variable to use later in the script. The script works, but....  I would like to be able to get it setup using 'dialog'. I found out that  'dialog --inputbox' will direct the output to 'stderr' and in order to get that input as a variable you have to direct it to a file and then retrieve it. The code I found to explain this is:  #!/bin/bash dialog --inputbox \  "What is your username?" 0 0 2&gt; /tmp/inputbox.tmp.$$  retval=$?  input=`cat /tmp/inputbox.tmp.$$`  rm -f /tmp/inputbox.tmp.$$  case $retval in 0)  echo "Your username is '$input'";; 1)  echo "Cancel pressed.";;  esac   I see that it is sending the sdterr to the /tmp/inputbox.tmp.$$ with 2>, but the output file looks like 'inputbox.tmp.21661'. When I try and cat the file it gives me an error. So I am still unable to get the user input from the --inputbox as a variable.   Example Script:   echo "  What app would you like to remove? "  read dead_app  sudo apt-get remove --purge $dead_app   So as you can see it is a basic script. Is it even possible to get the variable as a word from dialog --inputbox?