If we we dig a hole from north pole to the south pole of the Earth and we throw a ball in this hole where would it stop? Will it come back on the surface or it will stop at the centre?
...And you jumped in.  What would happen when you got to the middle of the Earth? Would you gradually slow down, until you got to the middle and once you were in middle would every direction feel like it was up?
How does \fontsize{}{} work? Determine accuracy of model which estimates probability of event How to re-install http windows service I replaced apache webserver with http(WINHTTP windows service) for use virtual hosts feature. But I was missing  http(WINHTTP windows service) which I previously removed.I  now want to  reinstall this service for use print spooler. PhD without previous academic degree: truth or myth? How to *disable* automatic reboots in Windows 10? I just ran into the problem of embedding fonts while trying to publish with lulu.com. Although everyone apparently is 'supposed' to handle those 35 standard fonts for some strange reason they won't accept pdf's without them included. So one way that according to  is supposed to work (I haven't tried yet, but hopefully it does work) is to convert the pdf to ps and then back to pdf and include the fonts at that time:  pdftops file.pdf ps2pdf14 -dPDFSETTINGS=/prepress file.ps   But this feels at least to me like the wrong way of doing things. Is there some way of passing the parameter directly to pdflatex to tell it to embed those fonts?   And, if not -- How do we go about getting such a feature? (Because it can't only be me who has this sort of problems) Entire one-to-one functions are linear Can we prove that every entire one-to-one function is linear? When reading about  on the OALD, I saw the following note:     The difference between someone and anyone is the same as the difference between  and . Look at the notes there.   The note that I read for some is the following:     In negative sentences and questions any is usually used instead of some:           I don't want any more vegetables.     Is there any wine left?           However, some is used in questions that expect a positive reply:           Would you like some milk in your coffee?     Didn't you borrow some books of mine?      Does that apply to someone too? Should I use someone in a question when I am expecting a positive answer?      Does someone know the answer? Difference between pts and tty This option, which was present in the "Mouse and Touchpad" settings panel in previous versions, is for some reason absent in 16.04 LTS. Does anyone know why this is, and/or how to fix it? Thanks. Prove $0! = 1$ from first principles Electromagnetic waves in vacuum If there is no source then also there is electromagnetic waves described by Maxwell equation. how if there is no source then existence of EM waves. What gives energy to this EM  waves. Is it vacuum fluctuation or something else? Density of ring of algebraic integers in $\mathbb C$ Clearly, $\mathbb Z$ is not dense in $\mathbb Q$ (and not dense in $\mathbb C$).  But why is the ring of algebraic integers $\overline{\mathbb Z}$ dense in $\overline{\mathbb Q}$?  In particular, if this is so, it is dense in $\mathbb C$. How bad for TeX is omitting braces {}, even if the result is the same? Sometimes writing braces and omitting them produces the same result:  \tilde{\psi}  \mathrm{e}^{\mathrm{i} \pi}   vs  \tilde \psi   \mathrm e^{\mathrm i \pi}   Or (taken from Werner's comment below)   \frac{1}{2} vs \frac12   If that's the case, how bad for the quality of my code is omitting them? Of course, if one compiles a pair of formulas, there is no difference. But, since I ignore how TeX works, my point is: if one writes long codes with these habits,   doesn't TeX go somehow crazy because I'm not writing as it expects?   For instance, does it have any effect on how fast are long documents compiled? Any reason to keep them? I have a multi-line equation that I want to have matching sized parentheses. The advice I read online was to use \left( equation \right. \\ left. rest-of-equation \right) . However, this syntax leaves first half of the equation unaware of what is in the second half. For example, if you include a square root term after the break, the second parenthesis will be larger than the opening parenthesis. When you are using the aligned environment to split a long equation this can look somewhat offputting.    Compare the top equation to the bottom one. The parentheses match in size for the bottom equation, but the left hand parentheses for the top one is  noticeably smaller.  Top Code:   \begin{aligned}[t]   \gamma_{\text{u}} + \frac{1}{108}   \left(57\gamma_{\text{er}} \right. &amp;+  38\gamma_{\text{se}}\\ &amp; {}\pm  \left.\sqrt{2601 \gamma_{\text{er}}^2 + 3648  \gamma_{\text{er}}\gamma_{\text{se}} + 1444 \gamma_{\text{se}}^2}  \right)   \end{aligned}   Bottom Code:  \begin{aligned}[t] \gamma_{\text{u}} + \frac{1}{16} \left(9\gamma_{\text{er}}  +  6\gamma_{\text{se}} \pm  \sqrt{49 \gamma_{\text{er}}^2 + 76 \gamma_{\text{er}}\gamma_{\text{se}} + 36 \gamma_{\text{se}}^2} \right) \end{aligned} Google Chrome PPA upgrade invalid signature Explicit formula for Bernoulli numbers by using only the recurrence relation It is not hard to show, by induction on $m\in\mathbb N$, that there exist a sequence $(B_n)_{n\geq0}$ of rational numbers such that  $$\sum_{k=1}^nk^m=\frac1{m+1}\sum_{k=0}^m\binom{m+1}kB_k\,n^{m+1-k},\ \style{font-family:inherit;}{\text{for all}}\ n\geq1\,.$$  These are the Bernoulli numbers of the second kind, that is, $B_1=+1/2$. A corollary of the proof (by induction) of the fact above is a recurrence formula for such numbers $B_n$, which are known as Bernoulli numbers:  $$\sum_{k=0}^{n-1}\binom nkB_k=0\,.\tag{$\ast$}$$  On the other hand, there are a number of explicit formulae for $B_n$, which are obtained using the equality $\frac x{e^x-1}=\sum_{n=0}^\infty B_n\,\frac{x^n}{n!}$; see  and . For example:  $$B_n=\sum_{k=0}^n\frac1{k+1}\sum_{r=0}^k(-1)^r\binom krr^n\,.\tag{$\ast\ast$}$$  Is there some clever way to manipulate the recurrence $(\ast)$ in order to obtain $(\ast\ast)$? I have an Asus N76VB notebook with Ubuntu 14.04 and TLP for power managment. However, the fan is always on. It's not really loud, but it's annoying. My CPU usage is around 1-2%. It's clocked at 1.20 GHz.  I've added acpi=force to my boot parameters but it doesn't change anything.  /proc/acpi/fan: No such file or directory /proc/acpi/thermal_zone: No such file or directory   I've loaded all Asus ACPI modules.  lsmod | grep asus:  asus_nb_wmi            16990  0  asus_wmi               24191  1 asus_nb_wmi sparse_keymap          13948  1 asus_wmi video                  19476  2 i915,asus_wmi wmi                    19177  2 mxm_wmi,asus_wmi   Somehow, it can read the temperatures.  sensors:  acpitz-virtual-0 Adapter: Virtual device temp1:        +43.0°C  (crit = +108.0°C)  coretemp-isa-0000 Adapter: ISA adapter Physical id 0:  +44.0°C  (high = +87.0°C, crit = +105.0°C) Core 0:         +44.0°C  (high = +87.0°C, crit = +105.0°C) Core 1:         +42.0°C  (high = +87.0°C, crit = +105.0°C) Core 2:         +39.0°C  (high = +87.0°C, crit = +105.0°C) Core 3:         +39.0°C  (high = +87.0°C, crit = +105.0°C)  asus-isa-0000 Adapter: ISA adapter temp1:        +43.0°C     I really hope someone knows how to solve this. Almost all information I could find was about saving power to create less heat.    I got Intel and NVIDIA (GeForce 740M) graphics but I'm almost anytime on Intel.  $ sudo lshw -c display   *-display                       description: VGA compatible controller        product: 3rd Gen Core processor Graphics Controller        vendor: Intel Corporation        physical id: 2        bus info: pci@0000:00:02.0        version: 09        width: 64 bits        clock: 33MHz        capabilities: msi pm vga_controller bus_master cap_list rom        configuration: driver=i915 latency=0        resources: irq:43 memory:f7400000-f77fffff memory:d0000000-dfffffff ioport:f000(size=64)     fwts fan: Accidental chown under / as root ́╗┐' is not recognized as an internal or external command When executing certain files (mainly batch) using PsExec I get these weird ́╗┐' symbols before my command. My initial thought was, that I were using wrong encoding, but after checking, I realized that all my files were using UTF-8.