Analog clock with same hands - sometimes one can't tell time
After swapping the positions of the hour and the minute hand, when will a clock still give a valid time?
Can [sic] be used to highlight a punctuational error?    In the sentence below, the bracketed sic would obviously denote that the punctuation preceding it was an error &mdash; that is, a semicolon should supplant the comma. Has anybody ever seen this usage, and would you support it?     The sun is high, [sic] put on some sunblock. Find the value of a given integral sequence: $I_n=\int_{0}^{1}(1-x^2)^ndx$ Let $(I_n)_{n \geq 1}$ be a sequence such that: $$I_n = \int_0^1 (1-x^2)^n dx$$  Find the value of $I_n$ (The solution is $\frac{2}{3} \cdot \frac{4}{5} \cdot ... \cdot \frac{2n}{2n+1}$).  I've tried using the binomial expansion of $(1-x^2)^n$ but I couldn't get the proper answer.  Thank you! Generating data with a given sample covariance matrix I'm trying to run a gunicorn_django process in supervisor but it always exits immediately, giving this error:   INFO exited: my_app (exit status 1; not expected) INFO received SIGCLD indicating a child quit INFO gave up: my_app entered FATAL state, too many start retries too quickly   My server script looks like this:  #!/bin/bash set -e LOGFILE=/var/log/gunicorn/my_app.log LOGDIR=$(dirname $LOGFILE) NUM_WORKERS=3 USER=my-www-user GROUP=my-www-user cd /home/my-www-user/my_app source /home/my-www-user/.virtualenvs/my_app/bin/activate test -d $LOGDIR || mkdir -p $LOGDIR gunicorn_django -w $NUM_WORKERS --debug \  --user=$USER --group=$GROUP \  --log-level=debug --log-file=$LOGFILE 2&gt;&gt;$LOGFILE\  --pythonpath=my_app --settings=settings.active \  my_app.wsgi:application   And my supervisor config looks like this:  [program:my_app] directory=/home/my-www-user/my_app/ user=my-www-user command=/home/my-www-user/my_app/server.sh stdout_logfile=/var/log/supervisor/my_app.log stderr_logfile=/var/log/supervisor/my_app-error.log autostart=true autorestart=true   When I su into the my-www-user account the server starts normally. When I do sudo supervisorctl start my_app it simply hangs until I do CTRL-c, then I find the error above in the supervisord.log file.  Does anyone have a clue about what I am missing? Double Negation in C++ I just came onto a project with a pretty huge code base.   I'm mostly dealing with C++ and a lot of the code they write uses double negation for their boolean logic.    if (!!variable &amp;&amp; (!!api.lookup("some-string"))) {        do_some_stuff();  }                                      I know these guys are intelligent programmers, it's obvious they aren't doing this by accident.   I'm no seasoned C++ expert, my only guess at why they are doing this is that they want to make absolutely positive that the value being evaluated is the actual boolean representation. So they negate it, then negate that again to get it back to its actual boolean value.   Is this correct, or am I missing something? Generate t distributed random variable in matlab How can we generate t distributed random variables with given mean and covariance in matlab. trnd is a function in matlab but we can get random variable with different degrees of freedom but how to get random variable with given mean and covariance? Proof that $\mathrm{ker}(f^*) = \mathrm{im}(f)^{\perp} $ Where $ f: V \rightarrow V  $ is a linear operator on an inner product space $V$, I'm trying to show that $$ \mathrm{ker}(f^*) = \mathrm{im}(f)^{\perp} $$  i.e. the Kernel of the adjoint is equal to the orthogonal complement of the image of f.  I taking the inner product of $f(v)$, where $v \in V$  and an arbitary element of the kernel, $k \in \mathrm{ker}(f^*) $  $$\langle f(v), k\rangle = \langle v, f^*(k)\rangle = \langle v, 0\rangle = 0$$  And then taking the inner product of $f(v)$ with $w$, where $w \in  \mathrm{im}(f)^{\perp}$  By definition  of the orthogonal complement to the image of f,   $$ \langle f(v), w\rangle = 0 $$  My question is, now that we have   $$ \langle f(v), k\rangle = \langle f(v), w\rangle = 0 $$  What can we conclude? I would like to conclude that because $w$ and $k$ are arbitary elements of their respective subspaces, that these must be equal, i.e. $ \mathrm{ker}(f^*) = \mathrm{im}(f)^{\perp} $  However, I am not sure this is mathematically sound, is that conclusion valid or are there any technical barriers or additional statements that would have to be made to make that watertight? When you add an image strip to the Video Sequence Editor, it stretches/shrinks your image to fit the full output frame.  How can I add an image at its original resolution?  For example, if I add a 60x60 pixel image, it should appear very small in the final 1080p render. I am wondering if we should use  or  for buttons and headings in websites and web/mobile apps? Title Case: Manage my Account Delete my Account  Sentence case: Manage my account Delete my account  In  I found the recommendation 'choose your style and be consistent'. This is it? Aren't there any other (additional) recommendations or sources. Like for specific use cases or apps where the one style would be preferred over the other? Edit: The question refers primarily to English, but differences in other languages are also good to know. How to modify font for all text fields? Decode Base64 data in Java I have an image that is Base64 encoded. What is the best way to decode that in Java? Hopefully using only the libraries included with Sun Java 6. How to add a browser tab icon (favicon) for a website? How can I check the available version of a package in the repositories? How can I check the version of the available package in the Ubuntu repositories without installing it? MATLAB/OCTAVE Extracting elements from different sized vectors in a cell array How can I Remove .DS_Store files from a Git repository? How can an ordered pair be expressed as a set? From Drupal 8 beta 6 (released today), I have this error :     Error message UnexpectedValueException: Untrusted Host "localhost" in   Symfony\Component\HttpFoundation\Request->getHost() (line 1221 of   core/vendor/symfony/http-foundation/Symfony/Component/HttpFoundation/Request.php).   I use this local url to call my site:   Inside my setting file, I have:       $settings['trusted_host_patterns'] = array(         'theming\.dev$',      );   Note, this error is displayed only when I uncomment this lines:   if (file_exists(__DIR__ . '/settings.local.php')) {    include __DIR__ . '/settings.local.php';  }   What is the problem please ? Thanks. biblatex: multiple bibliographies categorised by different .bib files biblatex supports multiple bibliographies by looking up the 1) entry type, 2) keyword, or 3) category.  This is all fine, but in the use case of primary sources and secondary sources: 1) the 'type' method doesn't work, 2) it is quite tedious to key in the 'primary' and 'secondary' keywords for each .bib entry, and 3) declaring the sorting by category would entail typing all the primary keys in the document.  So, if I'm storing all my primary bib entries in one .bib file, and secondary one in another, is there a bit to tell biblatex to assign a keyword or category automatically to all the entries from that bib file as it imports them?  Done this way, entries can be easily swapped to and from the primary and secondary .bib files without fiddling individual keywords, and I don't have to type out all the primary and/or secondary entries into categories in each document. What determines which pokemon you are allowed to place at a gym? So I defeated a Team Valor gym earlier today using my highest cp Pidgeot. It turned grey, so I went to claim it with that Pidgeot, except it wouldn't let me. What determines which pokemon you are allowed to place at a gym? Is it just those who have participated in a battle can't? Is there a time period for it? What about training at a friendly gym? Does this impact anything? How to parse hundred html source code files in shell?