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Is there a Windows standard way to do things such as "start fan", "decrease speed" or the like, from C/C++?  I have a suspicion it might be ACPI, but I am a frail mortal and cannot read that kind of documentation.  Edit: e.g. Windows 7 lets you select in your power plan options such as "passive cooling" (only when things get hot?) vs. "active cooling" (keep the CPU proactively cool?). It seems the OS does have a way to control the fan generically. Difference between float and decimal data type Is there a C pre-processor which eliminates #ifdef blocks based on values defined/undefined? I know that symlinks have a separated inode from the original file and that they only point for the inode containing the data. My question is, where is the hardlink name stored if there's no field in the inode structure refering to "name". I know that this could be a a relatively easy question, but as all hardlinks have the same inode number i assume that no inode is created when creating a hard link. ASP.NET MVC controller actions that return JSON or partial html I am trying to create controller actions which will return either JSON or partial html depending upon a parameter. What is the best way to get the result returned to an MVC page asynchronously? Find the image of (1,1,1) by T Question: Find the image of (1,1,1) by T  $$T(x,y,z) = (y,6y,x+y+z)$$   I found the standard matrix to be:   \begin{bmatrix}0&amp;1&amp;0\\0&amp;6&amp;0\\1&amp;1&amp;1\end{bmatrix}  I'm confused on how to approach this question.   In order to find the image is it possible to inverse the values of it's standard matrix?  Would I able to use the identity matrix of 3 and inverse the values of that to find the image?    Any help will be greatly appreciated. Why does the square root of a square involve the plus-minus sign? If $\sqrt{x^2}$ can be simplified as follows:  $\sqrt{x^2} = (x^2)^\frac{1}{2} = x^{\frac{2}{1}\times\frac{1}{2}} =x^\frac{2}{2} = x^1 = x$  Then why would $\sqrt{x^2} = \pm x$? Basic mathematical induction regarding inequalities These are just the examples from my textbook, but I don't think it did not explain well.  One of the problem was to prove the inequality   $$n&lt;2^n$$  for all integers $n$.  I understand we assume if $P(n)$ is true, $P(k+1)$ is true.  Thus $k+1&lt; 2^{k+1}$  But in the text book, they added one more line that I don't understand:  $$k+1&lt;2^k+1 \le 2^k+2^k=2\cdot2^k=2^{k+1}$$  I understand  $$k+1&lt;2^{k+1}$$  But how do I know $2^k+1$ is larger than $k+1$, and smaller than $2^{k+1}$?  I have one another example just in case,  proving $2^n&lt;n!$ using induction.  $$2^{k+1}=2\cdot 2^k&lt;2\cdot k!&lt;(k+1)k!=(k+1)!$$  I understand we should start with $2^{k+1}&lt;(k+1)!$, but  Where did $2\cdot k!$ come from? Textbook says it came from inductive hypothesis, but I still don't get it.  Please advise. In the double-slit experiment of electrons (observed by photons), is it correct to say the collapse is caused by the momentum of the photons? I'm working off the article, . I think it's well-written, but I'm not convinced about this part:     So what is causing the change in the particle’s behaviour?      In the example given above, when electrons are fired at a fluorescent screen, when we bombard the electrons with photons the interaction changes the state of the system catastrophically as, despite lacking mass, photons do carry momentum.   Here the author strongly implicates the momentum of photons as being responsible for the collapse. But is that correct to say?  I have read that the  verified that obscuring which-way information restores wave-like behavior. So it feels to me it's more about some "outer" state (perhaps well-characterized as "information") that we don't yet understand that collapses the system, not per se the photon-electron interaction.  Or am I wrong, and in fact for example, the process of obscuring in the quantum eraser experiments somehow "undoes" the photon-electron interaction or restores the quantum state through another interaction? Why do my LED lights stay on, even when the switch is off? I have two LED lamps in my corridor, and when I switch them off, they keep emitting light (not very strong, but it's annoying at night).  What can it be? How can I fix it? Which airlines allow in-cabin pets on transatlantic flights? Suppose $K/F$ is an extension field, and $E_1$ and $E_2$ are two intermediate subfields of finite degree. Let $E$ be the subfields of $K$ generated by $E_1$ and $E_2$. I'm trying to prove that $$ [E:F]\leq[E_1:F][E_2:F].$$  Since $E_1$ and $E_2$ are finite extensions, I suppose they have bases $\{a_1,\dots,a_n\}$ and $\{b_1,\dots,b_m\}$, respectively. If $E_1=F$ or $E_2=F$, then the inequality is actually equality, so I suppose both are proper extension fields. I think $E=F(a_1,\dots,a_n,b_1,\dots,b_m)$. Since $\{a_1,\dots,a_n,b_1,\dots,b_m\}$ is a spanning set for $E$ over $F$,  $$[E:F]\leq n+m\leq nm=[E_1:F][E_2:F]$$ since $m,n&gt;1$.  Is this sufficient? I'm weirded out since the problem did not ask to show $[E:F]\leq [E_1:F]+[E_2:F]$ which I feel will generally be a better upper bound. Show uncountable set of real numbers has a point of accumulation Show that every uncountable set of real numbers has a point of accumulation. Format not available in tag wiki excerpt For example, :   Format like bold or italic are not available , so it leaves ugly text there:  **This tag is *extremely* ambiguous. Consider using other tags instead.**    Does this need to get fixed, or it's not supported and the tag-wiki needs to be format-free? Orange squares appearing on render? Should I submit https:// and http:// in Google Search Console both with and without the www? In my site I'm redirecting everything (http://, http://www., https://) to https://www.example.com.  Google webmaster tools says: Make sure you add both "www" and "non-www" versions for your site. Also, if you use the HTTPS protocol, add those variations as well.  So I've added all the FOUR versions to google webmaster tools. Is this a correct process? Word or phrase for making something seem better by comparison What is a word or phrase that expresses the idea of purposely making something seem better by comparison? For example, lemon Starburst was created to make the cherry flavor seem that much tastier. How can I find out the size of a block device, such as /dev/sda? Running ls -l gives no useful information. How can I profile a multithread program in Python? I'm developing an inherently multithreaded module in Python, and I'd like to find out where it's spending its time. cProfile only seems to profile the main thread. Is there any way of profiling all threads involved in the calculation? The question is:     When $f(x+1)-f(x)=f'(x)$, what are the solutions for $f(x)$?   The most obvious solution is a linear function of the form $f(x)=ax+b$. Is this the only solution?  Edit  I should add that $f:\mathbb R\to\mathbb R$ to the question.