Today one question pop up into my mind... What will happen if Earth spinning about its axis and around the sun will start moving in reverse direction... Whether it will affect us... What are all things will change?
In the Futurama episode "" they save the world by rotating the Earth backwards saying it shouldn't matter (which direction Earth rotates). If Earth rotated clockwise and remained in it's current counter-clockwise orbit around the Sun, would it affect anything beyond the direction the constellations move across the sky?
Why do some people use $+\infty$ instead of $\infty$? Why do some people use $+\infty$ instead of $\infty$? Because we usually denote minus infinity as $-\infty$, I think it is sufficient to denote plus infinity as $\infty$. Are there any reasons for this notation? I saw that many people majoring analysis use like $\int_0^{+\infty}$ or $\sum_{j=1}^{+\infty}$ or $\bigcup_{j=1}^{+\infty}$ which is not related to the unsigned infinity. I am trying to find the correct opposite of a delegate in the context of a person being a representative of someone else that have allowed or chosen them to be their delegate. What would you call that "someone else?" The only word I could find is a delegator (which isn't a real word in English) or assigner, but they are technical words rather than descriptive.    Any other word I could use?    Think of it in a sentence like this:       Here is a list of all the delegates in the company.   But that is the list of their _ _ _ _ _ (what can go here?).   I am trying to avoid fillers such as:  bosses, agents, managers, etc. Requesting an active user page In my opinion, providing us with an active user page that shows the list of recent active users is useful as we can monitor the active users without visiting each user profile.  The list can be arranged in a grid of m rows by n columns and accompanied by labels representing the their reputations (and other info that you think they are important) and activities  such as "seen 2 minutes ago".  The following figure illustrates my idea. I am sorry. There is a typo in the following figure, Active must be changed to active to make it parallel to the other existing labels.     I think it is not too difficult to implement this. By adding a new action method and editing the view, done!  Of course it is not urgently requested feature. If it is useful, it can be put in the development to-do list so it can be implemented together with other useful requests at once.  Any responses are welcome! Regardless of how difficult it is, could you explain whether or not there are negative effects of this request? Down voting without informative comments looks barbaric. :-)  Edit:  If it is about user privacy, why is there a "seen 2 minutes ago" in the user profile page? I don't think there is a difference if we implement this feature. How do I back up AWS S3 and EBS to a non-Amazon provider? We've centered most of our operations on AWS, and love the ease of use there. However, every once in a while, the paranoid side of my brain wonders ?  Within the Amazon ecosystem, we have a pretty good backup plan: We keep most static data in S3. EBS volumes are snapshotted nightly. However, true paranoia would mean backing up to a provider outside the Amazon ecosystem. How do you handle doing this? I'm especially interested in backing up EBS snapshots and S3 contents. Bonus points for backing up RDS. Why does main method in Java always need arguments? How do you sort a dictionary by value? I often have to sort a dictionary, consisting of keys &amp; values, by value. For example, I have a hash of words and respective frequencies, that I want to order by frequency.  There is a SortedList which is good for a single value (say frequency), that I want to map it back to the word.   orders by key, not value. Some resort to a , but is there a cleaner way? Formula for completing the square? My math teacher said that this was the formula for completing the square.  Original function: $$ax^2 + bx + c$$ Completed square: $$a\left(x + \frac{b}{2a}\right)^2 - \frac{b^2}{4a} + c$$  However, using this formula I'm not getting the same answers that I would get just by determining the stuff myself.  Is this correct? Limit $\lim_{x \to \infty}{\sin{\sqrt{x+1}}-\sin{\sqrt{x}}}$ I want to compute $$\lim_{x \to \infty}{\sin{\sqrt{x+1}}-\sin{\sqrt{x}}}.$$  Is it OK how I want to do?    $$\sin{\sqrt{x+1}}-\sin{\sqrt{x}}=2\sin{\frac{\sqrt{x+1}-\sqrt{x}}{2}}\cos{\frac{\sqrt{x+1}+\sqrt{x}}{2}}=2\sin{\frac{1}{2(\sqrt{x+1}+\sqrt{x})}}\cos{\frac{\sqrt{x+1}+\sqrt{x}}{2}}$$  I'm not surem but I want to say that $$|\cos \frac{\sqrt{x+1}-\sqrt{x}}{2}| \leq 1$$ $$\sin{\frac{1}{2(\sqrt{x+1}+\sqrt{x})}} \to 0 \mbox{ when } x \to \infty$$ So the limit is $0$ ?  I thinks is not because  if I say that $ \displaystyle|\sin{\frac{1}{2(\sqrt{x+1}+\sqrt{x})}}| \leq 1$ I will obtain that another limit than $0$.   Thanks :) What is the terminal's graphic API? How can certain programs set background and font colors, write characters to the same location on screen (e.g. to the third row, fifth column) more than once?  Some examples are the progress bar displayed by curl google.com &gt; a, some installation screens and nearly any text editor. Unix Truncate Column in csv file Prove there exists $a\in \Bbb{R}$ such that $f'(a)=0$. Let $f$ be differentiable on $\Bbb{R}$ and let $\lim_\limits{x\to \infty}f(x)=\lim_\limits{x\to -\infty}f(x)=0$. Prove there exists $a\in \Bbb{R}$ such that $f'(a)=0$.  Attempt: If $f$ is constant we are done. Otherwise, $f$ is not constant. Suppose there is no such $a$. Then, in particular, $f$ has no extremum $\implies$ $f$ has no point where is goes from increasing to decreasing or from decreasing to increasing. $f$ is continuous since it is differentiable. Hence, since $\lim_\limits{x\to \infty}f(x)=\lim_\limits{x\to -\infty}f(x)=0$, $f$ must be constant. A contradiction. Therefore either $f$ is constant and $f'(x)=0$ everywhere, or $f$ has an extremum at $x=a$ and $f'(a)=0$.   I feel like my attempt is not formal enough, any correction?  I would appreciate your help. What do you call a sick person who is lying in bed? what is a thyristor As part of my 2330 lv3 am required to know about thyristors. I just want to confirm my understanding is correct. A thyristor is basically similar to a transistor, only it stays switched on when it's trigged for as long as there isn't a break in the circuit it's switching. Am I correct? Own table of contents? Repeatedly taking differences on a polynomial yields the factorial of its degree? How to adjust the gap between figure and caption within the same subfloat My question is:  How to adjust the gap between figure and caption within the same subfloat  Not the gap between two subfloat.  For the following example:  \begin{figure}     \centering     \subfloat[A]{\includegraphics[ scale=0.5]{images/a.jpg}}     \vspace{-10pt}     \subfloat[B]{\includegraphics[scale=0.5]{images/b.jpg}}     \vspace{-10pt}     \caption{}\label{fig:online_test} \end{figure}   I got the following figure:    The sub-caption of (a) is too close to the sub-figure B. I hope the caption (a) to stay closer to sub-figure A. How can I adjust the space between the caption and figure within a subfloat?  Thank you all for helping me and I would prefer a solution for subfloat, instead of using other packages. But I would also appreciate a solution of using other packages.   I know my question looks similar to . But please make it clear. I'm asking for how to adjust the gap between figure and caption within a subfloat, not the gap between two subfloat. That is, the gap between the caption "a" and the figure "A"  Thank you. Verbatim environment that can break long lines? I want to generate a PDF of user-submitted text using LaTeX. To handle crazy user input, I first thought about using the verbatim package, but of course it doesn't break up too long lines. Is there some package that works similar to verbatim (i.e., accept any input) but formats the text nicely? I'm having trouble understanding how to access each individual result returned from a subquery. The picture shows the code which:   takes fields and objects chosen by a user and assigns them to String variables, the string vars are used to query a dynamic query string, the query string is feed into a database.query and the result is stored in an array I can individually access each of the query results from this array (parent object results),  But I have not been able to individually access the subquery results.   If I feed the subquery results into an array...something like:  SObject[] c = p.get(i).getSObjects(childO);   I still can't get to each individual child record per parent. I can only see all child records per each parent. I need to get to each child record per adult, so that I can roll up results.  Can anyone help?  // These strings will be populated dynamically from a VF page String parentO  = 'Account'; String parentF  = 'Products_Purchased__c'; String childO   = 'Opportunity';     if(childO  == 'Opportunity'){ childO = 'Opportunities'; } String childF   = 'Product_Type__c';  // create dynamic SOQL query string String query = 'SELECT id, (select ' +childF+ ' from ' +childO+') FROM ' +parentO;  // query and store 33 results in variable p SObject[] p = Database.query(query);  for(Integer i = 0; i &lt; p.size(); i++){     system.debug('Parent result from SOQL query: ' +p[i]);     if(p.get(i).getSObjects(childO) &lt;&gt; null){         system.debug('Child result(s) from SOQL query: ' +p.get(i).getSObjects(childO));         system.debug('Child field: ' +c.get(i).get(childF));     } } Let $V$ be spherically symmetric and $W$ i.i.d. Gaussian. Then $E[V|V+W=t]=g(\|t\|)$ A random vector $V \in \mathbb{R}^n$ is said to be spherically symmetric. If for every orthogonal matrix  $A$   the distribution of $AV$ is the same as the distribution of $V$.   My question: Let $W$ be  i.i.d. zero mean Gaussian random variable.     Can we show that  for a spherically symmetric $V$ the conditional expectation  \begin{align} E[V|V+W=t]=   g(\|t\|).  \end{align}  That is the conditional expectation is only a function of the magnitude.   My attempt:  \begin{align} E[V|V+W=t]= \int  V  \frac{f_W(t-v)}{f_{V+W}(t)} dP_V(v)= \frac{\int  v  f_W(t-v) dP_V(v)}{f_{V+W}(t)}= \frac{E[ V  f_W(t-V) ]}{f_{V+W}(t)} \end{align}  Therefore, we can show that the two functions in the above ratio only depend on $\|t\|$.   Observe that we can write $t= \|t\| u_t$  where $u_t$ is a unit vector. Then, for any orthogonal matrix $A$ \begin{align} f_{V+W}(t)=f_{V+W}(\|t\|, u_t)&amp;= \frac{1}{(2\pi)^{n/2}} E[ e^{-\frac{\|t-V  \|^2}{2}} ]\\ &amp;= \frac{1}{(2\pi)^{n/2}} E[ e^{-\frac{\|t-AV  \|^2}{2}} ]\\ &amp;= \frac{1}{(2\pi)^{n/2}} E[ e^{-\frac{\|tA^{-1}-V  \|^2}{2}} ]\\ &amp;= \frac{1}{(2\pi)^{n/2}} E[ e^{-\frac{\|t A^T-V  \|^2}{2}} ]\\ &amp;= f_{V+W}(tA^T)\\ &amp;= f_{V+W}(\|t\|,  u_t A^T) \end{align}  Since, $A$ was arbitrary  we have that $f_{V+W}(t)=h(\|t\|)$(i.e., only depends on the magnitute).  Now I am not sure how to show that $E[ V  f_W(t-V) ]$ only depends on $\|t\|$? When should a verb be followed by a gerund instead of an infinitive? Some verbs are followed by ing, e.g. I enjoy swimming. We can't say I enjoy to swim. Likewise, some verbs are followed by to, e.g. I decided to make a plan.   Which particular verbs are followed by ing and to? Can you please provide a list for that?  Moreover, which verbs can be followed by both without having the meaning changed?